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Key research themes
1. How can rewriting basic equations reduce non-linearity in inverse scattering problems to improve quantitative reconstructions?
This research theme investigates mathematical reformulations of the fundamental inverse scattering equations, especially various forms of the Lippmann-Schwinger equation, to reduce the intrinsic non-linearity of inverse scattering problems. By recasting the scattering models into alternative formulations and hybrid approaches, researchers aim to mitigate false solutions, improve the stability and convergence of solution algorithms, and enhance quantitative reconstructions without reliance on prior information. These rewritings often involve integral equation transformations, contrast source inversion (CSI) methods, and the concept of virtual experiments, providing new insights into conditioning and solution refinement.
Key finding: The paper demonstrates that by employing three distinct reformulations of the Lippmann-Schwinger equation—including the contrast source extended Born (CS-EB) model, the NIE family, and the Y0 model—the degree of non-linearity... Read more
Key finding: The authors develop a hybrid inversion technique that incorporates an inhomogeneous Green's function encoding background knowledge into a qualitative linear sampling method and a quantitative contrast source inversion (CSI)... Read more
Key finding: This work reformulates the iterative Born approximation (IBA) as a feedforward neural network with layers corresponding to scattering iterations, enabling efficient gradient computation via error backpropagation. The approach... Read more
2. What is the impact of model dimensionality (2D vs 3D) and measurement configuration on resolution and imaging performance in linear inverse scattering?
This theme addresses how the choice between two-dimensional and three-dimensional scattering models affects the achievable spatial resolution and reconstruction quality within linear inverse scattering frameworks, especially under the Born approximation. It encompasses theoretical analyses using spectral methods and singular value decomposition (SVD), examines various measurement geometries (e.g., multimonostatic, multistatic, single-view), and provides numerical validations using full-wave data. The results inform practical imaging system design decisions, highlighting conditions where simpler 2D models suffice or where full 3D models are necessary to retain accuracy, particularly in noisy environments.
Key finding: This paper shows through singular value decomposition (SVD) analysis and point spread function (PSF) evaluations that 2D and 3D linear inverse scattering models under the Born approximation provide near-identical resolution... Read more
Key finding: Focusing on near and far-field single-frequency multi-view inverse scattering of cylindrical dielectric objects, especially in medical imaging contexts, this study presents an analytical approximation and numerical validation... Read more
3. How can direct sampling and moment-based methods provide robust, efficient approaches for inverse scattering with limited data and enhance reconstruction quality?
This research focus centers on developing and analyzing computationally efficient, non-iterative methods for inverse scattering problems that require minimal a priori information and can work with constrained measurement configurations such as near-field point source data or phaseless observations. Direct sampling methods utilize qualitative indicators constructed from measured scattered fields to rapidly localize scatterers. Moment methods and positivity constraints are leveraged to establish exact bounds and stability in one-dimensional scattering scenarios. These approaches contribute practical solutions for rapid imaging and enhanced robustness against incomplete or noisy data.
Key finding: The work proposes an iterative numerical scheme to recover compactly supported potentials in Schrödinger operators from phaseless scattering data combined with measurements in the presence of known background objects. The... Read more
Key finding: Applying positivity constraints derived from the classical theory of moments, this study establishes rigorous bounds on one-dimensional finite-range potential scattering amplitudes. The scattering wave function's moments form... Read more