397 research outputs found
Operational Rate-Distortion Performance of Single-source and Distributed Compressed Sensing
We consider correlated and distributed sources without cooperation at the
encoder. For these sources, we derive the best achievable performance in the
rate-distortion sense of any distributed compressed sensing scheme, under the
constraint of high--rate quantization. Moreover, under this model we derive a
closed--form expression of the rate gain achieved by taking into account the
correlation of the sources at the receiver and a closed--form expression of the
average performance of the oracle receiver for independent and joint
reconstruction. Finally, we show experimentally that the exploitation of the
correlation between the sources performs close to optimal and that the only
penalty is due to the missing knowledge of the sparsity support as in (non
distributed) compressed sensing. Even if the derivation is performed in the
large system regime, where signal and system parameters tend to infinity,
numerical results show that the equations match simulations for parameter
values of practical interest.Comment: To appear in IEEE Transactions on Communication
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
Highly Robust Error Correction by Convex Programming
This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal x â â^n (a block of n pieces of information) to a remote receiver. We ask whether it is possible to transmit this information reliably when a fraction of the transmitted codeword is corrupted by arbitrary gross errors, and when in addition, all the entries of the codeword are contaminated by smaller errors (e.g., quantization errors).
We show that if one encodes the information as Ax where A â
â^(m x n) (m â„ n) is a suitable coding matrix, there are two decoding schemes that allow the recovery of the block of n pieces of information x with nearly the same accuracy as if no gross errors occurred upon transmission (or equivalently as if one had an oracle supplying perfect information about the sites and amplitudes of the gross errors). Moreover, both decoding strategies are very concrete and only involve solving simple convex optimization programs, either a linear program or a second-order cone program. We complement our study with numerical simulations showing that the encoder/decoder pair performs remarkably well
Highly robust error correction by convex programming
This paper discusses a stylized communications problem where one wishes to
transmit a real-valued signal x in R^n (a block of n pieces of information) to
a remote receiver. We ask whether it is possible to transmit this information
reliably when a fraction of the transmitted codeword is corrupted by arbitrary
gross errors, and when in addition, all the entries of the codeword are
contaminated by smaller errors (e.g. quantization errors).
We show that if one encodes the information as Ax where A is a suitable m by
n coding matrix (m >= n), there are two decoding schemes that allow the
recovery of the block of n pieces of information x with nearly the same
accuracy as if no gross errors occur upon transmission (or equivalently as if
one has an oracle supplying perfect information about the sites and amplitudes
of the gross errors). Moreover, both decoding strategies are very concrete and
only involve solving simple convex optimization programs, either a linear
program or a second-order cone program. We complement our study with numerical
simulations showing that the encoder/decoder pair performs remarkably well.Comment: 23 pages, 2 figure
A robust compressive sensing based technique for reconstruction of sparse radar scenes
Cataloged from PDF version of article.Pulse-Doppler radar has been successfully applied to surveillance and tracking of both moving and
stationary targets. For efficient processing of radar returns, delayâDoppler plane is discretized and FFT
techniques are employed to compute matched filter output on this discrete grid. However, for targets
whose delayâDoppler values do not coincide with the computation grid, the detection performance
degrades considerably. Especially for detecting strong and closely spaced targets this causes miss
detections and false alarms. This phenomena is known as the off-grid problem. Although compressive
sensing based techniques provide sparse and high resolution results at sub-Nyquist sampling rates,
straightforward application of these techniques is significantly more sensitive to the off-grid problem.
Here a novel parameter perturbation based sparse reconstruction technique is proposed for robust delayâ
Doppler radar processing even under the off-grid case. Although the perturbation idea is general and can
be implemented in association with other greedy techniques, presently it is used within an orthogonal
matching pursuit (OMP) framework. In the proposed technique, the selected dictionary parameters are
perturbed towards directions to decrease the orthogonal residual norm. The obtained results show that
accurate and sparse reconstructions can be obtained for off-grid multi target cases. A new performance
metric based on KullbackâLeibler Divergence (KLD) is proposed to better characterize the error between
actual and reconstructed parameter spaces. Increased performance with lower reconstruction errors are
obtained for all the tested performance criteria for the proposed technique compared to conventional
OMP and 1 minimization techniques.
© 2013 Elsevier Inc. All rights reserve
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