35 research outputs found
Channel-Optimized Vector Quantizer Design for Compressed Sensing Measurements
We consider vector-quantized (VQ) transmission of compressed sensing (CS)
measurements over noisy channels. Adopting mean-square error (MSE) criterion to
measure the distortion between a sparse vector and its reconstruction, we
derive channel-optimized quantization principles for encoding CS measurement
vector and reconstructing sparse source vector. The resulting necessary optimal
conditions are used to develop an algorithm for training channel-optimized
vector quantization (COVQ) of CS measurements by taking the end-to-end
distortion measure into account.Comment: Published in ICASSP 201
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
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
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
Stable Recovery Of Sparse Vectors From Random Sinusoidal Feature Maps
Random sinusoidal features are a popular approach for speeding up
kernel-based inference in large datasets. Prior to the inference stage, the
approach suggests performing dimensionality reduction by first multiplying each
data vector by a random Gaussian matrix, and then computing an element-wise
sinusoid. Theoretical analysis shows that collecting a sufficient number of
such features can be reliably used for subsequent inference in kernel
classification and regression.
In this work, we demonstrate that with a mild increase in the dimension of
the embedding, it is also possible to reconstruct the data vector from such
random sinusoidal features, provided that the underlying data is sparse enough.
In particular, we propose a numerically stable algorithm for reconstructing the
data vector given the nonlinear features, and analyze its sample complexity.
Our algorithm can be extended to other types of structured inverse problems,
such as demixing a pair of sparse (but incoherent) vectors. We support the
efficacy of our approach via numerical experiments