Sparse Representation of Multiple Signals

Signal Processing, 2015

Motivated by the fact that the signals tend to have a representation biased towards their own classes, we propose a novel Sparse Representation-based Classifier (SRC) named Class Specific Sparse Representation-based Classifier (CSSRC), which incorporates the class information in the representation learning. Unlike the conventional SRC algorithms, CSSRC defines each class as a group and then impels these groups to compete for representing the test sample. To achieve such property, CSSRC imposes a L 1-norm constraint to the classes for compulsively selecting the most relevant classes and introduces a L 2-norm constraint to the samples belonging to the same class for making sure that all homogeneous samples can be sufficiently exploited for representation. Since CSSRC is a typical structure sparse representation issue, it can be efficiently solved by the convex optimization. Seven popular visual and audio signal databases are employed for evaluation. The results demonstrate its effectiveness in comparison with the state-of-the-art classifiers.

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

IEEE Journal of Selected Topics in Signal Processing, 2000

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.

IEEE Transactions on Image Processing, 2009

Sparse signals representation, analysis, and sensing, has received a lot of attention in recent years from the signal processing, optimization, and learning communities. On one hand, the learning of overcomplete dictionaries that facilitate a sparse representation of the image as a liner combination of a few atoms from such dictionary, leads to state-of-the-art results in image and video restoration and image classification. On the other hand, the framework of compressed sensing (CS) has shown that sparse signals can be recovered from far less samples than those required by the classical Shannon-Nyquist Theorem. The goal of this paper is to present a framework that unifies the learning of overcomplete dictionaries for sparse image representation with the concepts of signal recovery from very few samples put forward by the CS theory. The samples used in CS correspond to linear projections defined by a sampling projection matrix. It has been shown that, for example, a non-adaptive random sampling matrix satisfies the fundamental theoretical requirements of CS, enjoying the additional benefit of universality. On the other hand, a projection sensing matrix that is optimally designed for a certain signal class can further improve the reconstruction accuracy or further reduce the necessary number of samples. In this work we introduce a framework for the joint design and optimization, from a set of training images, of the overcomplete non-parametric dictionary and the sensing matrix. We show that this joint optimization outperforms both the use of random sensing matrices and those matrices that are optimized independently of the learning of the dictionary. The presentation of the framework and its efficient numerical optimization is complemented with numerous examples on classical image datasets.

2004

This report studies the effect of introducing a priori knowledge to recover sparse representations when overcomplete dictionaries are used. We focus mainly on Greedy algorithms and Basis Pursuit as for our algorithmic basement, while a priori is incorporated by suitably weighting the elements of the dictionary. A unique sufficient condition is provided under which Orthogonal Matching Pursuit, Matching Pursuit and Basis Pursuit are able to recover the optimally sparse representation of a signal when a priori information is available. Theoretical results show how the use of "reliable" a priori information can improve the performances of these algorithms. In particular, we prove that sufficient conditions to guarantee the retrieval of the sparsest solution can be established for dictionaries unable to satisfy the results of Gribonval and Vandergheynst [1] and Tropp [2]. As one might expect, our results reduce to the classical case of [1] and [2] when no a priori information is available. Some examples illustrate our theoretical findings.

In this specific work, Sparse Representation-Based Classification (SRC) can be extended intended for object identification. Proposed system consists of three main stages, sparse dictionary design, feature extraction and object detection. Initially a sparse dictionary will likely be designed along with large variety of different training images. It images incorporate various items including target image. Intended for feature extraction, if sparsity inside the recognition issue is correctly harnessed, the choice of features is not a critical issue. However the leading problem can be whether the volume of features can be sufficiently substantial and whether the sparse representation is the right way computed. Unconventional features such as down sampled images along with random projections perform equally well as typical features such as Eigen faces and Laplacian faces, as long because dimension in the feature place surpasses certain threshold, predicted from the theory of sparse representation in face recognition. Here down sampling process inside the images will likely be done. In assessment process the sparse dictionary typically determines the object among the other items. Extensive experiments will likely be conducted to help verify the efficacy in the proposed criteria, and corroborate the above mentioned claims.

In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method-the K-SVD algorithm-generalizing the K-means clustering process. K-SVD is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. The update of the dictionary columns is combined with an update of the sparse representations, thereby accelerating convergence. The K-SVD algorithm is flexible and can work with any pursuit method (e.g., basis pursuit, FOCUSS, or matching pursuit). We analyze this algorithm and demonstrate its results both on synthetic tests and in applications on real image data.

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2011 18th IEEE International Conference on Image Processing, 2011

We investigate an intrinsic and useful form of sparsity of color images that was largely overlooked in the literature of image/video processing. This sparsity of multispectral images is revealed and formulated by modeling the image formation process. The underlying new sparse representations of color images are general and can be exploited to improve the performance of existing image restoration algorithms, such as denoising, deblurring, and resolution upconversion.