5 research outputs found
Graded quantization for multiple description coding of compressive measurements
Compressed sensing (CS) is an emerging paradigm for acquisition of compressed
representations of a sparse signal. Its low complexity is appealing for
resource-constrained scenarios like sensor networks. However, such scenarios
are often coupled with unreliable communication channels and providing robust
transmission of the acquired data to a receiver is an issue. Multiple
description coding (MDC) effectively combats channel losses for systems without
feedback, thus raising the interest in developing MDC methods explicitly
designed for the CS framework, and exploiting its properties. We propose a
method called Graded Quantization (CS-GQ) that leverages the democratic
property of compressive measurements to effectively implement MDC, and we
provide methods to optimize its performance. A novel decoding algorithm based
on the alternating directions method of multipliers is derived to reconstruct
signals from a limited number of received descriptions. Simulations are
performed to assess the performance of CS-GQ against other methods in presence
of packet losses. The proposed method is successful at providing robust coding
of CS measurements and outperforms other schemes for the considered test
metrics
Graded quantization for multiple description coding of compressive measurements
Compressed sensing (CS) is an emerging paradigm for acquisition of compressed representations of a sparse signal. Its low complexity is appealing for resource-constrained scenarios like sensor networks. However, such scenarios are often coupled with unreliable communication channels and providing robust transmission of the acquired data to a receiver is an issue. Multiple description coding (MDC) effectively combats channel losses for systems without feedback, thus raising the interest in developing MDC methods explicitly designed for the CS framework, and exploiting its properties. We propose a method called Graded Quantization (CS-GQ) that leverages the democratic property of compressive measurements to effectively implement MDC, and we provide methods to optimize its performance. A novel decoding algorithm based on the alternating directions method of multipliers is derived to reconstruct signals from a limited number of received descriptions. Simulations are performed to assess the performance of CS-GQ against other methods in presence of packet losses. The proposed method is successful at providing robust coding of CS measurements and outperforms other schemes for the considered test metrics
Sparse linear regression with compressed and low-precision data via concave quadratic programming
We consider the problem of the recovery of a k-sparse vector from compressed
linear measurements when data are corrupted by a quantization noise. When the
number of measurements is not sufficiently large, different -sparse
solutions may be present in the feasible set, and the classical l1 approach may
be unsuccessful. For this motivation, we propose a non-convex quadratic
programming method, which exploits prior information on the magnitude of the
non-zero parameters. This results in a more efficient support recovery. We
provide sufficient conditions for successful recovery and numerical simulations
to illustrate the practical feasibility of the proposed method
Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices
One of the key issues in the acquisition of sparse data by means of
compressed sensing (CS) is the design of the measurement matrix. Gaussian
matrices have been proven to be information-theoretically optimal in terms of
minimizing the required number of measurements for sparse recovery. In this
paper we provide a new approach for the analysis of the restricted isometry
constant (RIC) of finite dimensional Gaussian measurement matrices. The
proposed method relies on the exact distributions of the extreme eigenvalues
for Wishart matrices. First, we derive the probability that the restricted
isometry property is satisfied for a given sufficient recovery condition on the
RIC, and propose a probabilistic framework to study both the symmetric and
asymmetric RICs. Then, we analyze the recovery of compressible signals in noise
through the statistical characterization of stability and robustness. The
presented framework determines limits on various sparse recovery algorithms for
finite size problems. In particular, it provides a tight lower bound on the
maximum sparsity order of the acquired data allowing signal recovery with a
given target probability. Also, we derive simple approximations for the RICs
based on the Tracy-Widom distribution.Comment: 11 pages, 6 figures, accepted for publication in IEEE transactions on
information theor