3,015 research outputs found
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
Quantization and Compressive Sensing
Quantization is an essential step in digitizing signals, and, therefore, an
indispensable component of any modern acquisition system. This book chapter
explores the interaction of quantization and compressive sensing and examines
practical quantization strategies for compressive acquisition systems.
Specifically, we first provide a brief overview of quantization and examine
fundamental performance bounds applicable to any quantization approach. Next,
we consider several forms of scalar quantizers, namely uniform, non-uniform,
and 1-bit. We provide performance bounds and fundamental analysis, as well as
practical quantizer designs and reconstruction algorithms that account for
quantization. Furthermore, we provide an overview of Sigma-Delta
() quantization in the compressed sensing context, and also
discuss implementation issues, recovery algorithms and performance bounds. As
we demonstrate, proper accounting for quantization and careful quantizer design
has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing
and Its Applications", 201
An Asynchronous Parallel Approach to Sparse Recovery
Asynchronous parallel computing and sparse recovery are two areas that have
received recent interest. Asynchronous algorithms are often studied to solve
optimization problems where the cost function takes the form , with a common assumption that each is sparse; that is, each
acts only on a small number of components of . Sparse
recovery problems, such as compressed sensing, can be formulated as
optimization problems, however, the cost functions are dense with respect
to the components of , and instead the signal is assumed to be sparse,
meaning that it has only non-zeros where . Here we address how one
may use an asynchronous parallel architecture when the cost functions are
not sparse in , but rather the signal is sparse. We propose an
asynchronous parallel approach to sparse recovery via a stochastic greedy
algorithm, where multiple processors asynchronously update a vector in shared
memory containing information on the estimated signal support. We include
numerical simulations that illustrate the potential benefits of our proposed
asynchronous method.Comment: 5 pages, 2 figure
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