2,619 research outputs found
Consistent Basis Pursuit for Signal and Matrix Estimates in Quantized Compressed Sensing
This paper focuses on the estimation of low-complexity signals when they are
observed through uniformly quantized compressive observations. Among such
signals, we consider 1-D sparse vectors, low-rank matrices, or compressible
signals that are well approximated by one of these two models. In this context,
we prove the estimation efficiency of a variant of Basis Pursuit Denoise,
called Consistent Basis Pursuit (CoBP), enforcing consistency between the
observations and the re-observed estimate, while promoting its low-complexity
nature. We show that the reconstruction error of CoBP decays like
when all parameters but are fixed. Our proof is connected to recent bounds
on the proximity of vectors or matrices when (i) those belong to a set of small
intrinsic "dimension", as measured by the Gaussian mean width, and (ii) they
share the same quantized (dithered) random projections. By solving CoBP with a
proximal algorithm, we provide some extensive numerical observations that
confirm the theoretical bound as is increased, displaying even faster error
decay than predicted. The same phenomenon is observed in the special, yet
important case of 1-bit CS.Comment: Keywords: Quantized compressed sensing, quantization, consistency,
error decay, low-rank, sparsity. 10 pages, 3 figures. Note abbout this
version: title change, typo corrections, clarification of the context, adding
a comparison with BPD
Reconstruction from Periodic Nonlinearities, With Applications to HDR Imaging
We consider the problem of reconstructing signals and images from periodic
nonlinearities. For such problems, we design a measurement scheme that supports
efficient reconstruction; moreover, our method can be adapted to extend to
compressive sensing-based signal and image acquisition systems. Our techniques
can be potentially useful for reducing the measurement complexity of high
dynamic range (HDR) imaging systems, with little loss in reconstruction
quality. Several numerical experiments on real data demonstrate the
effectiveness of our approach
Analysis-by-Synthesis-based Quantization of Compressed Sensing Measurements
We consider a resource-constrained scenario where a compressed sensing- (CS)
based sensor has a low number of measurements which are quantized at a low rate
followed by transmission or storage. Applying this scenario, we develop a new
quantizer design which aims to attain a high-quality reconstruction performance
of a sparse source signal based on analysis-by-synthesis framework. Through
simulations, we compare the performance of the proposed quantization algorithm
vis-a-vis existing quantization methods.Comment: 5 pages, Published in ICASSP 201
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
Distributed Quantization for Compressed Sensing
We study distributed coding of compressed sensing (CS) measurements using
vector quantizer (VQ). We develop a distributed framework for realizing
optimized quantizer that enables encoding CS measurements of correlated sparse
sources followed by joint decoding at a fusion center. The optimality of VQ
encoder-decoder pairs is addressed by minimizing the sum of mean-square errors
between the sparse sources and their reconstruction vectors at the fusion
center. We derive a lower-bound on the end-to-end performance of the studied
distributed system, and propose a practical encoder-decoder design through an
iterative algorithm.Comment: 5 Pages, Accepted for presentation in ICASSP 201
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