Tv-min and Greedy Pursuit for Constrained Joint Sparsity and Application to Inverse Scattering
نویسنده
چکیده
This paper proposes a general framework for compressed sensing of constrained joint sparsity (CJS) which includes total variation minimization (TV-min) as an example. The gradientand 2-norm error bounds, independent of the ambient dimension, are derived for the CJS version of Basis Pursuit and Orthogonal Matching Pursuit. As an application the results extend Candès, Romberg and Tao’s proof of exact recovery of piecewise constant objects with noiseless incomplete Fourier data to the case of noisy data.
منابع مشابه
Improved TV-CS Approaches for Inverse Scattering Problem
Total Variation and Compressive Sensing (TV-CS) techniques represent a very attractive approach to inverse scattering problems. In fact, if the unknown is piecewise constant and so has a sparse gradient, TV-CS approaches allow us to achieve optimal reconstructions, reducing considerably the number of measurements and enforcing the sparsity on the gradient of the sought unknowns. In this paper, ...
متن کاملCompressive Inverse Scattering I. High Frequency Simo Measurements
The inverse scattering problem with point scatterers and the single-input-multipleoutput (SIMO) measurements is analyzed by the compressed sensing techniques with and without the Born approximation. Three main results about (probabilistic) recoverability of sparse target by the L-optimization technique called Basis Pursuit (BP) are obtained in the high frequency limit. In the absence of noise, ...
متن کاملGradient Hard Thresholding Pursuit for Sparsity-Constrained Optimization
Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure for finding sparse solutions of underdetermined linear systems. This method has been shown to have strong theoretical guarantee and impressive numerical performance. In this paper, we generalize HTP from compressive sensing to a generic problem setup of sparsity-constrained convex optimization. The proposed algorithm ite...
متن کاملStagewise Weak Gradient Pursuits Part I: Fundamentals and Numerical Studies
Finding sparse solutions to underdetermined inverse problems is a fundamental challenge encountered in a wide range of signal processing applications, from signal acquisition to source separation. Recent theoretical advances in our understanding of this problem have further increased interest in their application to various domains. In many areas, such as for example medical imaging or geophysi...
متن کاملA Subspace Pursuit-based Iterative Greedy Hierarchical solution to the neuromagnetic inverse problem
Magnetoencephalography (MEG) is an important non-invasive method for studying activity within the human brain. Source localization methods can be used to estimate spatiotemporal activity from MEG measurements with high temporal resolution, but the spatial resolution of these estimates is poor due to the ill-posed nature of the MEG inverse problem. Recent developments in source localization meth...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012