Academia.eduAcademia.edu

Outline

Title
Abstract
The Analysis Model
Morphological Component Analysis
Background
Map & Mmse Estimators-The General Case
Estimator Performance-The General Case
Performance Analysis
Experimental Demonstration
Mmse and Map Bounds-A Summary
Summary and Conclusions
Analysis vs. Synthesis Models
An Analysis Signal Generation Model
Simulation Results
Methods
Results
Discussion
Real Data
Experiments and Results
Newton's Method for Covariance Selection
Treating a Block-Subproblem by Newton's Method
Gene Expression Analysis Experiments
3 the Linesearch Procedure
Introduction
Numerical Results
Conclusions
Conclusions and Future Work
Future Work
References
All Topics
Computer Science

Topics in Sparse Representation Modeling and Applications

Profile image of Javier TurekJavier Turek

2015

Abstract

First and foremost, I would like to thank my advisors Prof. Irad Yavneh and Prof. Michael Elad for their invaluable guidance and support during the course of my PhD studies. Irad's and Miki's enthusiasm and experience in research are a source of endless ideas. Their optimism, openness, brightness and clarity made working with them a unforgivable and enjoyable journey. Special thanks go to my colleagues and friends Dr. Eran Treister and Jeremias Sulam, with whom I had the honor to collaborate. I hope that we will find many more opportunities to collaborate in the future. I want to express my gratitude to my friends and colleagues for many inspiring discussions, helpful tips and fruitful conversations:

Related papers

Sparse Modeling for Image and Vision Processing
Jean Ponce

Foundations and Trends® in Computer Graphics and Vision, 2014

In recent years, a large amount of multidisciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection-that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.

View PDFchevron_right
Sparse modeling of high-dimensional data for learning and vision
Narendra Ahuja

2012

Sparse representations account for most or all of the information of a signal by a linear combination of a few elementary signals called atoms, and have increasingly become recognized as providing high performance for applications as diverse as noise reduction, compression, inpainting, compressive sensing, pattern classification, and blind source separation. In this dissertation, we learn the sparse representations of high-dimensional signals for various learning and vision tasks, including image classification, single image super-resolution, compressive sensing, and graph learning. Based on the bag-of-features (BoF) image representation in a spatial pyramid, we first transform each local image descriptor into a sparse representation, and then these sparse representations are summarized into a fixed-length feature vector over different spatial locations across different spatial scales by max pooling. The proposed generic image feature representation properly handles the large in-class variance problem in image classification, and experiments on object recognition, scene classification, face recognition, gender recognition, and handwritten digit recognition all lead to state-of-the-art performances on the benchmark datasets. We cast the image super-resolution problem as one of recovering a highresolution image patch for each low-resolution image patch based on recent sparse signal recovery theories, which state that, under mild conditions, a high-resolution signal can be recovered from its low-resolution version if the signal has a sparse representation in terms of some dictionary. We jointly learn the dictionaries for high-and low-resolution image patches and enforce them to have common sparse representations for better recovery. Furthermore, we employ image features and enforce patch overlapping constraints to improve prediction accuracy. Experiments show that the algorithm leads to surprisingly good results. Graph construction is critical for those graph-orientated algorithms designed for the purposes of data clustering, subspace learning, and semi-supervised learning. We model the graph construction problem, including neighbor selection and First, I would like to express profound gratitude to my adviser Professor Thomas Huang for all the guidance, advice, and support he has given me during my Ph.D. study at UIUC. For the last five and half years, I have been inspired by his vision and passion to research, his attention and curiosity to details, his dedication to the profession, his intense commitment to his work, and his humble and respectful personality. During this most important period in my career, I thoroughly enjoyed working with him, and what I have learned from him will benefit me for my whole life. I also would like to give my thanks to Professor Yi Ma for his suggestions and support for the last several years. I was deeply impressed and inspired by his passion and insights into research. I also feel very lucky to have had the chance to work with Dr. Kai Yu as a summer intern at NEC Laboratories America. From him, I learned not only techniques and skills but also his precious research insights. I am also very thankful to Professor Narendra Ahuja and Professor Zhi-Pei Liang for their advice and comments. I am fortunate to have them as my thesis committee members. During my Ph.D. study over the last five years, it has been a great honor for me to collaborate with Hasegawa-Johnson at UIUC, Professor Shuicheng Yan at

View PDFchevron_right
Sparse Representation For Image Prediction
C. Guillemot

2007

Publication in the conference proceedings of EUSIPCO, Poznan, Poland, 2007

View PDFchevron_right
A First Step to Convolutive Sparse Representation
Christian Jutten

Computing Research Repository, 2008

In this paper an extension of the sparse decomposition problem is considered and an algorithm for solving it is pre- sented. In this extension, it is known that one of the shifted versions of a signal s (not necessarily the original signal itself) has a sparse representation on an overcomplete dictionary, and we are looking for the sparsest representation among

View PDFchevron_right
Towards understanding sparse filtering: A theoretical perspective
Fabio Massimo Zennaro

Neural networks : the official journal of the International Neural Network Society, 2017

In this paper we present a theoretical analysis to understand sparse filtering, a recent and effective algorithm for unsupervised learning. The aim of this research is not to show whether or how well sparse filtering works, but to understand why and when sparse filtering does work. We provide a thorough theoretical analysis of sparse filtering and its properties, and further offer an experimental validation of the main outcomes of our theoretical analysis. We show that sparse filtering works by explicitly maximizing the entropy of the learned representations through the maximization of the proxy of sparsity, and by implicitly preserving mutual information between original and learned representations through the constraint of preserving a structure of the data. Specifically, we show that the sparse filtering algorithm implemented using an absolute-value non-linearity determines the preservation of a data structure defined by relations of neighborhoodness under the cosine distance. Fu...

View PDFchevron_right
Sparse coding in practice
A. Jepson

The goal in sparse coding is to seek a linear basis representation where each image is represented by a small number of active coefficients. The learning algorithm involves adapting a basis vector set while imposing a low-entropy, or sparse, prior on the output coefficients. Sparse coding applied on natural images has been shown to extract wavelet-like structure [9, 4]. However, our experience in using sparse coding for extracting multi-scale structure in object-specific ensembles, such as face images or images of a gesturing hand, has been negative. In this paper we highlight three points about the reliability of sparse coding for extracting the desired structure:´½µ using an overcomplete representation´¾µ projecting data into a low-dimensional subspace before attempting to resolve the sparse structure and´¿µ applying sparsity constraint on the basis elements, as opposed to the output coefficients.

View PDFchevron_right
Introduction to the issue on Adaptive Sparse Representation of Data and Applications in Signal and Image Processing
Panagiotis Tsakalides

IEEE Journal of Selected Topics in Signal Processing, 2000

View PDFchevron_right
Exploiting Statistical Dependencies in Sparse Representations for Signal Recovery
M. Elad

IEEE Transactions on Signal Processing, 2000

Signal modeling lies at the core of numerous signal and image processing applications. A recent approach that has drawn considerable attention is sparse representation modeling, in which the signal is assumed to be generated as a combination of a few atoms from a given dictionary. In this work we consider a Bayesian setting and go beyond the classic assumption of independence between the atoms. The main goal of this paper is to introduce a statistical model that takes such dependencies into account and show how this model can be used for sparse signal recovery. We follow the suggestion of two recent works and assume that the sparsity pattern is modeled by a Boltzmann machine, a commonly used graphical model. For general dependency models, exact MAP and MMSE estimation of the sparse representation becomes computationally complex. To simplify the computations, we propose greedy approximations of the MAP and MMSE estimators. We then consider a special case in which exact MAP is feasible, by assuming that the dictionary is unitary and the dependency model corresponds to a certain sparse graph. Exploiting this structure, we develop an efficient message passing algorithm that recovers the underlying signal. When the model parameters defining the underlying graph are unknown, we suggest an algorithm that learns these parameters directly from the data, leading to an iterative scheme for adaptive sparse signal recovery. The effectiveness of our approach is demonstrated on real-life signals -patches of natural images -where we compare the denoising performance to that of previous recovery methods that do not exploit the statistical dependencies.

View PDFchevron_right
Sparse representation of data
Frank-michael Schleif

2010

The amount of electronic data available today as well as its dimensionality and complexity increases rapidly in many scientific areas including biology, (bio-)chemistry, medicine, physics and its application fields like robotics, bioinformatics or multimedia technologies. Many of these data sets are very complex but have also a simple inherent structure which allows an appropriate sparse representation and modeling of such data with less or no information loss. Advanced methods are needed to extract these inherent but hidden information. Sparsity can be observed at different levels: sparse representation of data points using e.g. dimension- ality reduction for efficient data storage, sparse representation of full data sets using e.g. prototypes to achieve compact models for lifelong learning and sparse models of the underlying data structure using sparse encoding techniques. One main goal is to achieve a human-interpretable represen- tation of the essential information. Sparse repre...

View PDFchevron_right
An Efficient Algorithm for Sparse Representations with lp Data Fidelity Term
Brendt Wohlberg

2008

Basis Pursuit (BP) and Basis Pursuit Denoising (BPDN), well established techniques for computing sparse representations, minimize an 2 data fidelity term, subject to an 1 sparsity constraint or regularization term, by mapping the problem to a linear or quadratic program. BPDN with an 1 data fidelity term has recently been proposed, also implemented via a mapping to a linear program. We introduce an alternative approach via an Iteratively Reweighted Least Squares algorithm, providing computational advantages and greater flexibility in the choice of data fidelity term norm.

View PDFchevron_right

References (182)

  1. J. S. Turek, I. Yavneh, and M. Elad. On MMSE and MAP Denoising Under Sparse Repre- sentation Modeling Over a Unitary Dictionary. IEEE Transactions on Signal Processing, vol. 59, no. 8, pp. 3526-3535, Aug. 2011.
  2. J. S. Turek, I. Yavneh, and M. Elad. On MAP and MMSE Estimators for the Co-sparse Analysis Model. Digital Signal Processing, vol. 28, pp. 57-74, May 2014.
  3. J. S. Turek, I. Yavneh, and M. Elad. Clutter Mitigation on Echocardiography using Sparse Signal Separation. Accepted to International Journal in Biomedical Imaging, 2015.
  4. J. S. Turek, M. Elad, and I. Yavneh. Sparse Signal Separation with an Off-line Learned Dictionary for Clutter Reduction in Echocardiography. IEEE 28-th Convention of Electrical and Electronics Engineers in Israel, Dec. 2014.
  5. J. S. Turek, J. Sulam, M. Elad, and I. Yavneh. Fusion of Ultrasound Harmonic Imaging with Clutter Removal Using Sparse Signal Separation. 40-th IEEE International Confer- ence on Acoustics, Speech and Signal Processing 2015 (ICASSP 2015), Apr. 2015. (Equal Contribution)
  6. V. Abolghasemi, S. Ferdowsi, and S. Sanei. Blind separation of image sources via adaptive dictionary learning. IEEE Transactions on Image Processing, 21(6):2921- 2930, June 2012.
  7. M. Aharon and M. Elad. Sparse and redundant modeling of image content using an image-signature-dictionary. SIAM Journal on Imaging Sciences, 1(3):228-247, 2008.
  8. M. Aharon, M. Elad, and A. Bruckstein. K-SVD: An algorithm for designing overcom- plete dictionaries for sparse representation. IEEE Transactions on Signal Processing, 54(11):4311-4322, November 2006.
  9. L. Armijo. Minimization of functions having lipschitz continuous first partial derivatives. Pacific Journal of Mathematics, 16(1):1-3, 1966.
  10. O. Banerjee, L. El Ghaoui, and A. d'Aspremont. Model selection through sparse max- imum likelihood estimation for multivariate gaussian or binary data. The Journal of Machine Learning Research, 9:485-516, 2008.
  11. O. Banerjee, L. El Ghaoui, A. d'Aspremont, and G. Natsoulis. Convex optimization techniques for fitting sparse gaussian graphical models. In Proceedings of the 23rd International Conference on Machine learning (ICML), pages 89-96. ACM, 2006.
  12. R.G. Baraniuk, V. Cevher, and M.B. Wakin. Low-dimensional models for dimension- ality reduction and signal recovery: A geometric perspective. Proceedings of the IEEE, 98(6):959-971, 2010.
  13. A. Beck and M. Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1):183-202, 2009.
  14. Z. Ben-Haim, Y.C. Eldar, and M. Elad. Coherence-based performance guarantees for es- timating a sparse vector under random noise. IEEE Transactions on Signal Processing, 58(10):5030-5043, October 2010.
  15. Y. Bengio. Learning deep architectures for AI. Foundations and Trends in Machine Learning, 2(1):1-127, January 2009.
  16. Y. Bengio, A. Courville, and P. Vincent. Representation learning: A review and new perspectives. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(8):1798-1828, 2013.
  17. P.J. Bickel, Y. Ritov, and A.B. Tsybakov. Simultaneous analysis of lasso and dantzig selector. The Annals of Statistics, 37(4):pp. 1705-1732, 2009.
  18. J.A. Bilmes. Factored sparse inverse covariance matrices. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), vol- ume 2, pages II1009-II1012 vol.2, 2000.
  19. J.M. Bioucas-Dias and M.A.T. Figueiredo. A new twist: Two-step iterative shrink- age/thresholding algorithms for image restoration. IEEE Transactions on Image Pro- cessing, 16(12):2992-3004, December 2007.
  20. S. Bjaerum, H. Torp, and K. Kristoffersen. Clutter filter design for ultrasound color flow imaging. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 49(2):204-216, February 2002.
  21. S. Bjaerum, H. Torp, and K. Kristoffersen. Clutter filters adapted to tissue motion in ultrasound color flow imaging. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 49(6):693-704, 2002.
  22. J. Bobin, Y. Moudden, J.-L. Starck, and M. Elad. Morphological diversity and source separation. IEEE Signal Processing Letters, 13(7):409-412, July 2006.
  23. A. Bruckstein, D. Donoho, and M. Elad. From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Review, 51(1):34-81, February 2009.
  24. A. Buades, B. Coll, and J.-M Morel. A non-local algorithm for image denoising. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), volume 2, pages 60-65, 2005.
  25. J.-F. Cai, H. Ji, Z. Shen, and G.-B. Ye. Data-driven tight frame construction and image denoising. Applied and Computational Harmonic Analysis, 37(1):89 -105, 2014.
  26. J.-F. Cai, S. Osher, and Z. Shen. Split bregman methods and frame based image restoration. Multiscale Modeling & Simulation, 8(2):337-369, 2010.
  27. T.T. Cai, L. Wang, and G. Xu. Stable recovery of sparse signals and an oracle inequality. IEEE Transactions on Information Theory, 56(7):3516 -3522, July 2010.
  28. C. Caiati, N. Zedda, C. Montaldo, R. Montisci, and S. Iliceto. Contrast-enhanced transthoracic second harmonic echo doppler with adenosine: A noninvasive, rapid and effective method for coronary flow reserve assessment. Journal of the American College of Cardiology, 34(1):122 -130, 1999.
  29. E. Candès and T. Tao. The dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics, 35(6):2313-2351, December 2007.
  30. E.J. Candès. Modern statistical estimation via oracle inequalities. Acta Numerica, 15:257-325, May 2006.
  31. E.J. Candès and D.L. Donoho. Recovering edges in ill-posed inverse problems: opti- mality of curvelet frames. The Annals of Statistics, 30(3):784-842, June 2002.
  32. E.J. Candès, Y.C. Eldar, D. Needell, and P. Randall. Compressed sensing with coherent and redundant dictionaries. Applied and Computational Harmonic Analysis, 31(1):59- 73, 2011.
  33. E.J. Candès, X. Li, Y. Ma, and J. Wright. Robust principal component analysis? Journal of the ACM, 58(3):11:1-11:37, June 2011.
  34. S.S. Chen, D.L. Donoho, and M.A. Saunders. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 20(1):33-61, 1998.
  35. G.M. Chin, J. Nocedal, P.A. Olsen, and S.J. Rennie. Second order methods for opti- mizing convex matrix functions and sparse covariance clustering. IEEE Transactions on Audio, Speech, and Language Processing, 21(11):2244-2254, November 2013.
  36. G. Cloutier, D. Chen, and L.-G. Durand. A new clutter rejection algorithm for doppler ultrasound. IEEE Transactions on Medical Imaging, 22(4):530-538, 2003.
  37. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian. Image denoising by sparse 3- d transform-domain collaborative filtering. IEEE Transactions on Image Processing, 16(8):2080-2095, 2007.
  38. A. Danielyan, V. Katkovnik, and K. Egiazarian. Bm3d frames and variational image deblurring. IEEE Transactions on Image Processing, 21(4):1715-1728, 2012.
  39. A. d'Aspremont, O. Banerjee, and L. El Ghaoui. First-order methods for sparse co- variance selection. SIAM Journal on Matrix Analysis and Applications, 30(1):56-66, 2008.
  40. I. Daubechies. Ten Lectures on Wavelets. Society for Industrial and Applied Mathe- matics, 1992.
  41. I. Daubechies, M. Defrise, and C. De Mol. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications on pure and applied mathematics, 57(11):1413-1457, 2004.
  42. B. Deka and P.K. Bora. Removal of correlated speckle noise using sparse and overcom- plete representations. Biomedical Signal Processing and Control, 8(6):520-533, 2013.
  43. R. Demirli and J. Saniie. An efficient sparse signal decomposition technique for ultra- sonic signal analysis using envelope and instantaneous phase. In IEEE International Ultrasonics Symposium (IUS), pages 1503-1507, November 2008.
  44. R. Demirli and J. Saniie. Model-based estimation pursuit for sparse decomposition of ultrasonic echoes. Signal Processing, IET, 6(4):313-325, June 2012.
  45. A.P. Dempster. Covariance selection. Biometrics, pages 157-175, 1972.
  46. M.N. Do and M. Vetterli. Contourlets: a new directional multiresolution image repre- sentation. In Conference Record of the 36th Asilomar Conference on Signals, Systems and Computers, volume 1, pages 497-501, November 2002.
  47. A. Dobra, C. Hans, B. Jones, J.R. Nevins, G. Yao, and M. West. Sparse graphical models for exploring gene expression data. Journal of Multivariate Analysis, 90(1):196 -212, 2004. Special Issue on Multivariate Methods in Genomic Data Analysis.
  48. D.L. Donoho and M. Elad. On the stability of the basis pursuit in the presence of noise. Signal Processing, 86(3):511 -532, 2006. Sparse Approximations in Signal and Image Processing Sparse Approximations in Signal and Image Processing.
  49. D.L. Donoho and J.M. Johnstone. Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81(3):425-455, 1994.
  50. M. Elad. Why simple shrinkage is still relevant for redundant representations? IEEE Transactions on Information Theory, 52(12):5559-5569, December 2006.
  51. M. Elad. Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. Springer, 2010.
  52. M. Elad, B. Matalon, and M. Zibulevsky. Coordinate and subspace optimization meth- ods for linear least squares with non-quadratic regularization. Applied and Computa- tional Harmonic Analysis, 23(3):346 -367, 2007.
  53. M. Elad, P. Milanfar, and R. Rubinstein. Analysis versus synthesis in signal priors. Inverse Problems, 23(3):947, 2007.
  54. M. Elad, J.-L. Starck, P. Querre, and D.L. Donoho. Simultaneous cartoon and tex- ture image inpainting using morphological component analysis (MCA). Applied and Computational Harmonic Analysis, 19(3):340-358, 2005.
  55. M. Elad and I. Yavneh. A plurality of sparse representations is better than the sparsest one alone. IEEE Transactions on Information Theory, 55(10):4701-4714, 2009.
  56. K. Engan, S.O. Aase, and J. Hakon Husoy. Method of optimal directions for frame design. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), volume 5, pages 2443-2446, 1999.
  57. M.J. Fadili, J.-L. Starck, J. Bobin, and Y. Moudden. Image decomposition and separa- tion using sparse representations: An overview. Proceedings of the IEEE, 98(6):983-994, June 2010.
  58. S. Fischer, G. Cristobal, and R. Redondo. Sparse overcomplete gabor wavelet represen- tation based on local competitions. IEEE Transactions on Image Processing, 15(2):265- 272, February 2006.
  59. B.A. French, Y. Li, A.L. Klibanov, Z. Yang, and J.A. Hossack. 3D perfusion mapping in post-infarct mice using myocardial contrast echocardiography. Ultrasound in Medicine & Biology, 32(6):805-815, 2006.
  60. J. Friedman, T. Hastie, and R. Tibshirani. Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3):432-441, 2008.
  61. C.M. Gallippi and G.E. Trahey. Adaptive clutter filtering via blind source separation for two-dimensional ultrasonic blood velocity measurement. Ultrasonic Imaging, 24(4):193- 214, 2002.
  62. S. Geman and D. Geman. Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6(6):721-741, 1984.
  63. E. Gil-Rodrigo, J. Portilla, D. Miraut, and R. Suarez-Mesa. Efficient joint poisson-gauss restoration using multi-frame l2-relaxed-l0 analysis-based sparsity. In Proceedings of the 18th IEEE International Conference Image Processing (ICIP), pages 1385-1388, 2011.
  64. R. Giryes and M. Elad. Cosamp and SP for the cosparse analysis model. In Proceedings of the 20th European Signal Processing Conference (EUSIPCO-2012), pages 964-968, 2012.
  65. R. Giryes and M. Elad. RIP-based near-oracle performance guarantees for SP, CoSaMP, and IHT. IEEE Transactions on Signal Processing, 60(3):1465-1468, March 2012.
  66. R. Giryes, S. Nam, R. Gribonval, and M.E. Davies. Iterative Cosparse Projection Algorithms for the Recovery of Cosparse Vectors. In Proceedings of the 19th European Signal Processing Conference (EUSIPCO-2011), pages 1460-1464, Barcelona, Espagne, 2011.
  67. R. Gribonval. Should penalized least squares regression be interpreted as maximum a posteriori estimation? IEEE Transactions on Signal Processing, 59(5):2405-2410, May 2011.
  68. T.L. Griffiths and Z. Ghahramani. Infinite latent feature models and the indian buffet process. Technical Report GCNU TR 2005-001, Gatsby Computational Neuroscience Unit, 2005.
  69. S. Gupta, R.C. Chauhan, and S.C. Sexana. Wavelet-based statistical approach for speckle reduction in medical ultrasound images. Medical and Biological Engineering and Computing, 42(2):189-192, 2004.
  70. S. Hawe, M. Kleinsteuber, and K. Diepold. Cartoon-like image reconstruction via constrained p -minimization. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pages 717-720, 2012.
  71. S. Hawe, M. Kleinsteuber, and K. Diepold. Analysis operator learning and its applica- tion to image reconstruction. IEEE Transactions on Image Processing, 22(6):2138-2150, 2013.
  72. J. Honorio and T.S. Jaakkola. Inverse covariance estimation for high-dimensional data in linear time and space: Spectral methods for riccati and sparse models. In Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI), 2013.
  73. T. Hozumi, K. Yoshida, Y. Abe, R. Kanda, T. Akasaka, T. Takagi, T. Yagi, Y. Ogata, and J. Yoshikawa. Visualization of clear echocardiographic images with near field noise reduction technique: Experimental study and clinical experience. Journal of the Amer- ican Society of Echocardiography, 11(6):660-667, 1998.
  74. C.-J. Hsieh, I. Dhillon, P. Ravikumar, and A. Banerjee. A divide-and-conquer method for sparse inverse covariance estimation. In F. Pereira, C.J.C. Burges, L. Bottou, and K.Q. Weinberger, editors, Advances in Neural Information Processing Systems 25, pages 2330-2338. Curran Associates, Inc., 2012.
  75. C.-J. Hsieh and P. Olsen. Nuclear norm minimization via active subspace selection. In Proceedings of the 31st International Conference on Machine Learning (ICML), ICML '14, June 2014.
  76. C.-J. Hsieh, M.A. Sustik, I. Dhillon, P. Ravikumar, and R. Poldrack. Big & quic: Sparse inverse covariance estimation for a million variables. In C.J.C. Burges, L. Bot- tou, M. Welling, Z. Ghahramani, and K.Q. Weinberger, editors, Advances in Neural Information Processing Systems 26, pages 3165-3173. Curran Associates, Inc., 2013.
  77. C.-J. Hsieh, M.A. Sustik, I.S. Dhillon, and P.D. Ravikumar. Sparse inverse covariance matrix estimation using quadratic approximation. In J. Shawe-Taylor, R.S. Zemel, P.L. Bartlett, F. Pereira, and K.Q. Weinberger, editors, Advances in Neural Information Processing Systems 24, pages 2330-2338. Curran Associates, Inc., 2011.
  78. S. Huang, J. Li, L. Sun, J. Liu, T. Wu, K. Chen, A. Fleisher, E. Reiman, and J. Ye. Learning brain connectivity of alzheimer's disease from neuroimaging data. In Y. Ben- gio, D. Schuurmans, J.D. Lafferty, C.K.I. Williams, and A. Culotta, editors, Advances in Neural Information Processing Systems 22, pages 808-816. Curran Associates, Inc., 2009.
  79. J.A. Jensen. Field: A program for simulating ultrasound systems. Medical and Biological Engineering and Computing, 10th Nordic-Baltic Conference on Biomedical Imaging, 4(1):351-353, 1996.
  80. H. Ji, Y. Xu, and Z. Shen. Wavelet based restoration of images with missing or damaged pixels. East Asian Journal on Applied Mathematics, 1(2):108-131, 2011.
  81. A.P. Kadi and T. Loupas. On the performance of regression and step-initialized IIR clutter filters for color doppler systems in diagnostic medical ultrasound. IEEE Transac- tions on Ultrasonics, Ferroelectrics, and Frequency Control, 42(5):927-937, September 1995.
  82. G. Karypis and V. Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing, 20(1):359-392, 1998.
  83. S.M. Kay. Fundamentals of Statistical Signal Processing: Estimation Theory, volume I. Prentice Hall, 1993.
  84. D.E. Kruse and K.W. Ferrara. A new high resolution color flow system using an eigendecomposition-based adaptive filter for clutter rejection. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 49(12):1739-1754, December 2002.
  85. D. Labate, W.-Q. Lim, G. Kutyniok, and G. Weiss. Sparse multidimensional repre- sentation using shearlets. In Wavelets XI (Proceedings of SPIE), volume 5914, pages 254-262, 2005.
  86. H. Larochelle, Y. Bengio, J. Louradour, and P. Lamblin. Exploring strategies for train- ing deep neural networks. Journal of Machine Learning Research, 10:1-40, June 2009.
  87. E.G. Larsson and Y. Selen. Linear regression with a sparse parameter vector. IEEE Transactions on Signal Processing, 55(2):451-460, 2007.
  88. M.A. Lediju, B.C. Byram, and G.E. Trahey. Sources and characterization of clutter in cardiac b-mode images. In IEEE International Ultrasonics Symposium (IUS), pages 1419-1422, September 2009.
  89. M.A. Lediju, M.J. Pihl, S.J. Hsu, J.J. Dahl, C.M. Gallippi, and G.E. Trahey. Mag- nitude, origins, and reduction of abdominal ultrasonic clutter. In IEEE International Ultrasonics Symposium (IUS), pages 50-53, November 2008.
  90. M.A. Lediju, M.J. Pihl, S.J. Hsu, J.J. Dahl, C.M. Gallippi, and G.E. Trahey. A motion- based approach to abdominal clutter reduction. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 56(11):2437-2449, November 2009.
  91. L.A.F. Ledoux, P.J. Brands, and A.P.G. Hoeks. Reduction of the clutter component in doppler ultrasound signals based on singular value decomposition: A simulation study. Ultrasonic Imaging, 19(1):1-18, 1997.
  92. K.Y.E. Leung, M.G. Danilouchkine, M. van Stralen, N. de Jong, A.F.W. van der Steen, and J.G. Bosch. Probabilistic framework for tracking in artifact-prone 3D echocardio- grams. Medical Image Analysis, 14(6):750-758, 2010.
  93. L. Li and K.-C. Toh. An inexact interior point method for l-1 regularized sparse covari- ance selection. Mathematical Programming Computation, 2(3-4):291-315, 2010.
  94. S. Li, H. Yin, and L. Fang. Group-sparse representation with dictionary learning for medical image denoising and fusion. IEEE Transactions on Biomedical Engineering, 59(12):3450-3459, December 2012.
  95. Y. Li, C.D. Garson, Y. Xu, B.A. French, and J.A. Hossack. High frequency ultrasound imaging detects cardiac dyssynchrony in noninfarcted regions of the murine left ven- tricle late after reperfused myocardial infarction. Ultrasound in Medicine & Biology, 34(7):1063-1075, 2008.
  96. H. Liebgott, R. Prost, and D. Friboulet. Pre-beamformed RF signal reconstruction in medical ultrasound using compressive sensing. Ultrasonics, 53(2):525-533, 2013.
  97. Q. Liu, S. Wang, L. Ying, X. Peng, Y. Zhu, and D. Liang. Adaptive dictionary learning in sparse gradient domain for image recovery. IEEE Transactions on Image Processing, 22(12):4652-4663, 2013.
  98. H.-M. Lu, Y. Fainman, and R. Hecht-Nielsen. Image manifolds. In Proceedings of the SPIE, volume 3307 of Applications of Artificial Neural Networks in Image Processing III, pages 52-63, 1998.
  99. Y.M. Lu and M.N. Do. Multidimensional directional filter banks and surfacelets. IEEE Transactions on Image Processing, 16(4):918-931, April 2007.
  100. Y.M. Lu and M.N. Do. A theory for sampling signals from a union of subspaces. IEEE Transactions on Signal Processing, 56(6):2334-2345, June 2008.
  101. S. Mallat. A Wavelet Tour of Signal Processing. Academic Press, 3rd edition, December 2008.
  102. S.G. Mallat and Z. Zhang. Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing, 41(12):3397-3415, December 1993.
  103. G. Marsaglia. Conditional means and covariances of normal variables with singular covariance matrix. Journal of the American Statistical Association, 59(308):1203-1204, 1964.
  104. F.R. Mauldin, F. Viola, and W.F. Walker. Robust motion estimation using complex principal components. In IEEE International Ultrasonics Symposium (IUS), pages 2429-2432, 2009.
  105. F.W. Mauldin, D. Lin, and J.A. Hossack. The singular value filter: A general filter design strategy for PCA-based signal separation in medical ultrasound imaging. IEEE Transactions on Medical Imaging, 30(11):1951-1964, November 2011.
  106. R. Mazumder and T. Hastie. Exact covariance thresholding into connected components for large-scale graphical lasso. The Journal of Machine Learning Research, 13:781-794, 2012.
  107. D. Mele, O. Soukhomovskaia, E. Pacchioni, E. Merli, N. Avigni, L. Federici, R.A. Levine, and R. Ferrari. Improved detection of left ventricular thrombi and spontaneous echocontrast by tissue harmonic imaging in patients with myocardial infarction. Journal of the American Society of Echocardiography, 19:1373-1381, November 2006.
  108. O. Michailovich and D. Adam. A high-resolution technique for ultrasound harmonic imaging using sparse representations in gabor frames. IEEE Transactions on Medical Imaging, 21(12):1490-1503, December 2002.
  109. P. Moulin and J. Liu. Analysis of multiresolution image denoising schemes using gen- eralized gaussian and complexity priors. IEEE Transactions on Information Theory, 45(3):909-919, April 1999.
  110. S. Nam, M.E. Davies, M. Elad, and R. Gribonval. Cosparse analysis modeling -unique- ness and algorithms. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pages 5804-5807, 2011.
  111. S. Nam, M.E. Davies, M. Elad, and R. Gribonval. Recovery of cosparse signals with greedy analysis pursuit in the presence of noise. In Proceedings of the 4th IEEE In- ternational Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pages 361-364, 2011.
  112. S. Nam, M.E. Davies, M. Elad, and R. Gribonval. The cosparse analysis model and algorithms. Applied and Computational Harmonic Analysis, 34(1):30-56, 2013.
  113. B. K. Natarajan. Sparse approximate solutions to linear systems. SIAM Journal on Computing, 24(2):227-234, 1995.
  114. C.I. Nieblas, M.A. Alonso, R. Conte, and S. Villarreal. High performance heart sound segmentation algorithm based on matching pursuit. In IEEE Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE), pages 96-100, 2013.
  115. Q.g Nin, K. Chen, L. Yi, C. Fan, Y. Lu, and J. Wen. Image super-resolution via analysis sparse prior. IEEE Signal Processing Letters, 20(4):399-402, 2013.
  116. P.A. Olsen, O. Figen, J. Nocedal, and S.J. Rennie. Newton-like methods for sparse inverse covariance estimation. In F. Pereira, C.J.C. Burges, L. Bottou, and K.Q. Wein- berger, editors, Advances in Neural Information Processing Systems 25, pages 755-763. Curran Associates, Inc., 2012.
  117. B. Ophir, M. Elad, N. Bertin, and M.D. Plumbley. Sequential minimal eigenvalues -an approach to analysis dictionary learning. In Proceedings of the 19th European Signal Processing Conference (EUSIPCO-2011), Barcelona, Spain, August 2011.
  118. O. Oreifej, X. Li, and M. Shah. Simultaneous video stabilization and moving object detection in turbulence. IEEE Transactions on Pattern Analysis and Machine Intelli- gence, 35(2):450-462, 2013.
  119. Y.C. Pati, R. Rezaiifar, and P.S. Krishnaprasad. Orthogonal matching pursuit: recur- sive function approximation with applications to wavelet decomposition. In Conference Record of The 27th Asilomar Conference on Signals, Systems and Computers, pages 40-44 vol.1, November 1993.
  120. T. Peleg and M. Elad. Performance guarantees of the thresholding algorithm for the cosparse analysis model. IEEE Transactions on Information Theory, 59(3):1832-1845, 2013.
  121. T. Peleg, Y.C. Eldar, and M. Elad. Exploiting statistical dependencies in sparse rep- resentations for signal recovery. IEEE Transactions on Signal Processing, 60(5):2286- 2303, 2012.
  122. G. Peyré and J. Fadili. Learning analysis sparsity priors. In Proceedings of the 9th International Conference on Sampling, Theory and Applications (SAMPTA), page 1, 2011.
  123. G. Peyré, J. Fadili, and J.-L. Starck. Learning the morphological diversity. SIAM Journal on Imaging Sciences, 3(3):646-669, 2010.
  124. J. Portilla. Image restoration through l0 analysis-based sparse optimization in tight frames. In Proceedings of the 16th IEEE International Conference Image Processing (ICIP), pages 3909-3912, 2009.
  125. M. Protter, I. Yavneh, and M. Elad. Closed-form MMSE estimator for denoising signals under sparse reconstruction modeling. In Eleventh IEEEI conference, Eilat, Israel, December 2008.
  126. M. Protter, I. Yavneh, and M. Elad. Closed-form MMSE estimation for signal denoising under sparse representation modeling over a unitary dictionary. IEEE Transactions on Signal Processing, 58(7):3471-3484, July 2010.
  127. A.E. Raftery and S. Lewis. How many iterations in the Gibbs sampler. Bayesian statistics, 4(2):763-773, 1992.
  128. I. Ram, I. Cohen, and M. Elad. Patch-ordering-based wavelet frame and its use in inverse problems. IEEE Transactions on Image Processing, 23(7):2779-2792, July 2014.
  129. M. Ranzato, Y. Boureau, and Y. LeCun. Sparse feature learning for deep belief net- works. In Advances in Neural Information Processing Systems 20 (NIPS), pages 1185- 1192, 2007.
  130. B. Rolfs, B. Rajaratnam, D. Guillot, I. Wong, and A. Maleki. Iterative thresholding algorithm for sparse inverse covariance estimation. In F. Pereira, C.J.C. Burges, L. Bot- tou, and K.Q. Weinberger, editors, Advances in Neural Information Processing Systems 25, pages 1574-1582. Curran Associates, Inc., 2012.
  131. S. Roth and M.J. Black. Fields of experts. International Journal of Computer Vision, 82(2):205-229, 2009.
  132. R. Rubinstein, A.M. Bruckstein, and M. Elad. Dictionaries for sparse representation modeling. Proceedings of the IEEE, 98(6):1045-1057, June 2010.
  133. R. Rubinstein, T. Peleg, and M. Elad. Analysis K-SVD: A dictionary-learning algorithm for the analysis sparse model. IEEE Transactions on Signal Processing, 61(3):661-677, 2013.
  134. R. Rubinstein, M. Zibulevsky, and M. Elad. Efficient implementation of the K-SVD algorithm using batch orthogonal matching pursuit. Technical report, Dept. Computer Science, Technion, Israel, 2009.
  135. R. Rubinstein, M. Zibulevsky, and M. Elad. Double sparsity: Learning sparse dic- tionaries for sparse signal approximation. IEEE Transactions on Signal Processing, 58(3):1553-1564, March 2010.
  136. M. Rudelson and R. Vershynin. Sparse reconstruction by convex relaxation: Fourier and gaussian measurements. In Proceedings of the 40th Annual Conference on Information Sciences and Systems, pages 207-212, March 2006.
  137. H. Rue and L. Held. Gaussian Markov Random Fields: Theory and Applications, volume 104 of Monographs on Statistics and Applied Probability. Chapman & Hall, London, 2005.
  138. Y. Saad. Iterative methods for sparse linear systems, 2 nd edition. SIAM, 2003.
  139. M.F. Schiffner, T. Jansen, and G. Schmitz. Compressed sensing for fast image acquisi- tion in pulse-echo ultrasound. Biomedical Engineering-Biomedizinische Technik, 57(1), September 2012.
  140. P. Schniter, L.C. Potter, and J. Ziniel. Fast bayesian matching pursuit. In Information Theory and Applications Workshop, pages 326-333, 2008.
  141. I.W. Selesnick and M.A.T. Figueiredo. Signal restoration with overcomplete wavelet transforms: comparison of analysis and synthesis priors. In Proceedings of SPIE, volume 7446, pages 74460D-74460D-15, 2009.
  142. S. Shalev-Shwartz, A. Gonen, and O. Shamir. Large-scale convex minimization with a low-rank constraint. In Lise Getoor and Tobias Scheffer, editors, Proceedings of the 28th International Conference on Machine Learning (ICML), ICML '11, pages 329-336, New York, NY, USA, June 2011. ACM.
  143. E.P. Simoncelli and E.H. Adelson. Noise removal via bayesian wavelet coring. In Proceedings of the IEEE International Conference Image Processing (ICIP), volume 1, pages 379-382 vol.1, September 1996.
  144. J.-L. Starck, M. Elad, and D.L. Donoho. Redundant multiscale transforms and their application for morphological component separation. In Advances in Imaging and Elec- tron Physics, volume 132 of Advances in Imaging and Electron Physics, pages 287-348. Elsevier, 2004.
  145. J.-L. Starck, F. Murtagh, and J.M. Fadili. Sparse Image and Signal Processing. Cam- bridge University Press, 2010.
  146. M. Tanabe, B. Lamia, H. Tanaka, D. Schwartzman, M. R. Pinsky, and J. Gorcsan III. Echocardiographic speckle tracking radial strain imaging to assess ventricular dyssyn- chrony in a pacing model of resynchronization therapy. Journal of the American Society of Echocardiography, 21(12):1382-1388, 2008.
  147. T. Taxt and R. Jirik. Superresolution of ultrasound images using the first and sec- ond harmonic signal. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 51(2):163-175, February 2004.
  148. P.C. Tay, S.T. Acton, and J.A. Hossack. A transform method to remove ultrasound artifacts. In IEEE Southwest Symposium on Image Analysis and Interpretation (SSIAI), pages 110-114, 2006.
  149. P.C. Tay, S.T. Acton, and J.A. Hossack. A wavelet thresholding method to reduce ultrasound artifacts. Computerized Medical Imaging and Graphics, 35(1):42-50, 2011.
  150. A. Teske, B. De Boeck, P. Melman, G. Sieswerda, P. Doevendans, and M. Cramer. Echocardiographic quantification of myocardial function using tissue deformation imag- ing, a guide to image acquisition and analysis using tissue doppler and speckle tracking. Cardiovascular Ultrasound, 5(1):27, 2007.
  151. J.D. Thomas and D.N. Rubin. Tissue harmonic imaging: Why does it work? Journal of the American Society of Echocardiography, 11(8):803-808, August 1998.
  152. R. Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), pages 267-288, 1996.
  153. H. Torp. Clutter rejection filters in color flow imaging: a theoretical approach. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 44(2):417-424, March 1997.
  154. F. Tranquart, N. Grenier, V. Eder, and L. Pourcelot. Clinical use of ultrasound tissue harmonic imaging. Ultrasound in Medicine and Biology, 25(6):889 -894, 1999.
  155. E. Treister and J.S. Turek. A block-coordinate descent approach for large-scale sparse inverse covariance estimation. In Advances in Neural Information Processing Systems 27, pages 927-935. Curran Associates, Inc., 2014.
  156. E. Treister, J.S. Turek, and I. Yavneh. Multilevel framework for the sparse inverse covariance estimation. In Optimization Workshop (OPT) in Advances in Neural Infor- mation Processing Systems 27, 2014.
  157. E. Treister and I. Yavneh. A multilevel iterated-shrinkage approach to l 1 penalized least-squares minimization. IEEE Transactions on Signal Processing, 60(12):6319-6329, 2012.
  158. J.A. Tropp. Greed is good: algorithmic results for sparse approximation. IEEE Trans- actions on Information Theory, 50(10):2231-2242, 2004.
  159. Y. Tsaig and D.L. Donoho. Compressed sensing. IEEE Transactions on Information Theory, 52:1289-1306, 2006.
  160. P. Tseng and S. Yun. A coordinate gradient descent method for nonsmooth separable minimization. Mathematical Programming, 117(1-2):387-423, 2009.
  161. J.S. Turek, M. Elad, and I. Yavneh. Sparse signal separation with an off-line learned dictionary for clutter reduction in echocardiography. In Electrical Electronics Engineers in Israel (IEEEI), IEEE 28th Convention of, pages 1-5, December 2014.
  162. J.S. Turek, M. Elad, and I. Yavneh. Clutter mitigation in echocardiography using sparse signal separation. Accepted to International Journal in Biomedical Imaging, 2015.
  163. J.S. Turek, J. Sulam, M. Elad, and I. Yavneh. Fusion of ultrasound harmonic imag- ing with clutter removal using sparse signal separation. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2015.
  164. J.S. Turek, I. Yavneh, and M. Elad. On MMSE and MAP denoising under sparse repre- sentation modeling over a unitary dictionary. IEEE Transactions on Signal Processing, 59(8):3526-3535, August 2011.
  165. J.S. Turek, I. Yavneh, and M. Elad. On MAP and MMSE estimators for the co-sparse analysis model. Digital Signal Processing, 28(0):57 -74, 2014.
  166. J.S. Turek, I. Yavneh, M. Protter, and M. Elad. On MMSE and MAP de- noising under sparse representation modeling over a unitary dictionary. Tech- nical Report 2010-14, Dept. Computer Science, Technion, Israel, July 2010. http://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-info.cgi/2010/CS/CS-2010-14.
  167. S. Vaiter, G. Peyré, C. Dossal, and J. Fadili. Robust sparse analysis regularization. IEEE Transactions on Information Theory, 59(4):2001-2016, 2013.
  168. R.F. Wagner, S.W. Smith, J.M. Sandrik, and H. Lopez. Statistics of speckle in ul- trasound b-scans. IEEE Transactions on Sonics and Ultrasonics, 30(3):156-163, May 1983.
  169. Z. Wen, W. Yin, D. Goldfarb, and Y. Zhang. A fast algorithm for sparse reconstruc- tion based on shrinkage, subspace optimization, and continuation. SIAM Journal on Scientific Computing, 32(4):1832-1857, 2010.
  170. J. Wormann, S. Hawe, and M. Kleinsteuber. Analysis based blind compressive sensing. IEEE Signal Processing Letters, 20(5):491-494, 2013.
  171. S.J. Wright, R.D. Nowak, and M.A.T. Figueiredo. Sparse reconstruction by separable approximation. IEEE Transactions on Signal Processing, 57(7):2479-2493, July 2009.
  172. M. Yaghoobi, S. Nam, R. Gribonval, and M.E. Davies. Noise aware rator learning for approximately cosparse signals. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pages 5409-5412, 2012.
  173. M. Yaghoobi, S. Nam, R. Gribonval, and M.E. Davies. Constrained overcomplete anal- ysis operator learning for cosparse signal modelling. IEEE Transactions on Signal Processing, 61(9):2341-2355, 2013.
  174. A. Yu and L. Lovstakken. Eigen-based clutter filter design for ultrasound color flow imaging: a review. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 57(5):1096-1111, May 2010.
  175. A.C.H. Yu and R.S.C. Cobbold. Single-ensemble-based eigen-processing methods for color flow imaging -part I. the hankel-SVD filter. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 55(3):559-572, 2008.
  176. A.C.H. Yu and R.S.C. Cobbold. Single-ensemble-based eigen-processing methods for color flow imaging -part II. the matrix pencil estimator. IEEE Transactions on Ultra- sonics, Ferroelectrics, and Frequency Control, 55(3):573-587, 2008.
  177. Y. Zhang, L. Wang, Y. Gao, J. Chen, and X. Shi. Automatic de-noising of doppler ultrasound signals using matching pursuit method. In Justinian Rosca, Deniz Erdogmus, Jose C. Principe, and Simon Haykin, editors, Independent Component Analysis and Blind Signal Separation, volume 3889 of Lecture Notes in Computer Science, pages 519-526. Springer Berlin Heidelberg, 2006.
  178. Y. Zhou, H. Chen, J. Paisley, L. Ren, L. Li, Z. Xing, D. Dunson, G. Sapiro, and L. Carin. Nonparametric bayesian dictionary learning for analysis of noisy and incomplete images. IEEE Transactions on Image Processing, 21(1):130-144, January 2012.
  179. M. Zibulevsky and M. Elad. L1-l2 optimization in signal and image processing. IEEE Signal Processing Magazine, 27(3):76-88, May 2010.
  180. M. Zibulevsky and B. Pearlmutter. Blind source separation by sparse decomposition in a signal dictionary. Neural Computation, 13(4):863-882, April 2001.
  181. H. Zou and T. Hastie. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B, 67:301-320, 2005.
  182. G. Zwirn and S. Akselrod. Stationary clutter rejection in echocardiography. Ultrasound in Medicine and Biology, 32(1):43-52, 2006.

Related papers

Proceedings of the second" international Traveling Workshop on Interactions between Sparse models and Technology"(iTWIST'14)
Jerome Louveaux

iTWIST'14: international -Traveling Workshop on Interactions between Sparse models and Technology.

View PDFchevron_right
Proceedings of the third "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'16)
Marko Panic

2016

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/man...

View PDFchevron_right
Optimization algorithms for sparse representations and applications
Andrzej Cichocki

2006

We consider the following sparse representation problem, which is called Sparse Component Analysis: identify the matrices S ∈ IR n×N and A ∈ IR m×n (m ≤ n < N ) uniquely (up to permutation of scaling), knowing only their multiplication X = AS, under some conditions, expressed either in terms of A and sparsity of S (identifiability conditions), or in terms of X (Sparse Component Analysis conditions). A crucial assumption (sparsity condition) is that S is sparse of level k in sense that each column of S has at least k nonzero elements (k = 1, 2, ..., m − 1).

View PDFchevron_right
Sparse and Redundant Representations_ From Theory to Applications in Signal and Image Processing
Elham Alaee

The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.

View PDFchevron_right
Universal priors for sparse modeling
Federico Lecumberry

2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2009

Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many signal and image processing tasks. It is now well understood that the choice of the sparsity regularization term is critical in the success of such models. In this work, we use tools from information theory to propose a sparsity regularization term which has several theoretical and practical advantages over the more standard 0 or 1 ones, and which leads to improved coding performance and accuracy in reconstruction tasks. We also briefly report on further improvements obtained by imposing low mutual coherence and Gram matrix norm on the learned dictionaries.

View PDFchevron_right

Related topics

  • Computer Science
    • 580 California St., Suite 400
    San Francisco, CA, 94104
    © 2025 Academia. All rights reserved