6,403 research outputs found
Info-Greedy sequential adaptive compressed sensing
We present an information-theoretic framework for sequential adaptive
compressed sensing, Info-Greedy Sensing, where measurements are chosen to
maximize the extracted information conditioned on the previous measurements. We
show that the widely used bisection approach is Info-Greedy for a family of
-sparse signals by connecting compressed sensing and blackbox complexity of
sequential query algorithms, and present Info-Greedy algorithms for Gaussian
and Gaussian Mixture Model (GMM) signals, as well as ways to design sparse
Info-Greedy measurements. Numerical examples demonstrate the good performance
of the proposed algorithms using simulated and real data: Info-Greedy Sensing
shows significant improvement over random projection for signals with sparse
and low-rank covariance matrices, and adaptivity brings robustness when there
is a mismatch between the assumed and the true distributions.Comment: Preliminary results presented at Allerton Conference 2014. To appear
in IEEE Journal Selected Topics on Signal Processin
Methods for Quantized Compressed Sensing
In this paper, we compare and catalog the performance of various greedy quantized compressed sensing algorithms that reconstruct sparse signals from quantized compressed measurements. We also introduce two new greedy approaches for reconstruction: Quantized Compressed Sampling Matching Pursuit (QCoSaMP) and Adaptive Outlier Pursuit for Quantized Iterative Hard Thresholding (AOP-QIHT). We compare the performance of greedy quantized compressed sensing algorithms for a given bit-depth, sparsity, and noise level
One-Bit Compressed Sensing by Greedy Algorithms
Sign truncated matching pursuit (STrMP) algorithm is presented in this paper.
STrMP is a new greedy algorithm for the recovery of sparse signals from the
sign measurement, which combines the principle of consistent reconstruction
with orthogonal matching pursuit (OMP). The main part of STrMP is as concise as
OMP and hence STrMP is simple to implement. In contrast to previous greedy
algorithms for one-bit compressed sensing, STrMP only need to solve a convex
and unconstraint subproblem at each iteration. Numerical experiments show that
STrMP is fast and accurate for one-bit compressed sensing compared with other
algorithms.Comment: 16 pages, 7 figure
Performance Comparisons of Greedy Algorithms in Compressed Sensing
Compressed sensing has motivated the development of numerous sparse approximation algorithms designed to return a solution to an underdetermined system of linear equations where the solution has the fewest number of nonzeros possible, referred to as the sparsest solution. In the compressed sensing setting, greedy sparse approximation algorithms have been observed to be both able to recovery the sparsest solution for similar problem sizes as other algorithms and to be computationally efficient; however, little theory is known for their average case behavior. We conduct a large scale empirical investigation into the behavior of three of the state of the art greedy algorithms: NIHT, HTP, and CSMPSP. The investigation considers a variety of random classes of linear systems. The regions of the problem size in which each algorithm is able to reliably recovery the sparsest solution is accurately determined, and throughout this region additional performance characteristics are presented. Contrasting the recovery regions and average computational time for each algorithm we present algorithm selection maps which indicate, for each problem size, which algorithm is able to reliably recovery the sparsest vector in the least amount of time. Though no one algorithm is observed to be uniformly superior, NIHT is observed to have an advantageous balance of large recovery region, absolute recovery time, and robustness of these properties to additive noise and for a variety of problem classes. The algorithm selection maps presented here are the first of their kind for compressed sensing
Conjugate Gradient Iterative Hard Thresholding:\ud Observed Noise Stability for Compressed Sensing
Conjugate Gradient Iterative Hard Thresholding (CGIHT) for compressed sensing combines the low per iteration complexity of fast greedy sparse approximation algorithms with the improved convergence rates of more complicated, projection based algorithms. This article shows that CGIHT is robust to\ud
additive noise and is typically the fastest greedy algorithm in the presence of noise
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