239 research outputs found
TV-min and Greedy Pursuit for Constrained Joint Sparsity and Application to Inverse Scattering
This paper proposes a general framework for compressed sensing of constrained
joint sparsity (CJS) which includes total variation minimization (TV-min) as an
example. TV- and 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 Cand`es, Romberg and Tao's proof of exact
recovery of piecewise constant objects with noiseless incomplete Fourier data
to the case of noisy data.Comment: Mathematics and Mechanics of Complex Systems (2013
Compressive Sensing Theory for Optical Systems Described by a Continuous Model
A brief survey of the author and collaborators' work in compressive sensing
applications to continuous imaging models.Comment: Chapter 3 of "Optical Compressive Imaging" edited by Adrian Stern
published by Taylor & Francis 201
Joint Block-Sparse Recovery Using Simultaneous BOMP/BOLS
We consider the greedy algorithms for the joint recovery of high-dimensional
sparse signals based on the block multiple measurement vector (BMMV) model in
compressed sensing (CS). To this end, we first put forth two versions of
simultaneous block orthogonal least squares (S-BOLS) as the baseline for the
OLS framework. Their cornerstone is to sequentially check and select the
support block to minimize the residual power. Then, parallel performance
analysis for the existing simultaneous block orthogonal matching pursuit
(S-BOMP) and the two proposed S-BOLS algorithms is developed. It indicates that
under the conditions based on the mutual incoherence property (MIP) and the
decaying magnitude structure of the nonzero blocks of the signal, the
algorithms select all the significant blocks before possibly choosing incorrect
ones. In addition, we further consider the problem of sufficient data volume
for reliable recovery, and provide its MIP-based bounds in closed-form. These
results together highlight the key role of the block characteristic in
addressing the weak-sparse issue, i.e., the scenario where the overall sparsity
is too large. The derived theoretical results are also universally valid for
conventional block-greedy algorithms and non-block algorithms by setting the
number of measurement vectors and the block length to 1, respectively.Comment: This work has been submitted to the IEEE for possible publicatio
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