Structure-Based Bayesian Sparse Reconstruction

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical information (Gaussian or otherwise) to obtain near optimal estimates. In addition, we make use of the rich structure of the sensing matrix encountered in many signal processing applications to develop a fast sparse recovery algorithm. The computational complexity of the proposed algorithm is relatively low compared with the widely used convex relaxation methods as well as greedy matching pursuit techniques, especially at a low sparsity rate.Comment: 29 pages, 15 figures, accepted in IEEE Transactions on Signal Processing (July 2012

Super-resolution Line Spectrum Estimation with Block Priors

We address the problem of super-resolution line spectrum estimation of an undersampled signal with block prior information. The component frequencies of the signal are assumed to take arbitrary continuous values in known frequency blocks. We formulate a general semidefinite program to recover these continuous-valued frequencies using theories of positive trigonometric polynomials. The proposed semidefinite program achieves super-resolution frequency recovery by taking advantage of known structures of frequency blocks. Numerical experiments show great performance enhancements using our method.Comment: 7 pages, double colum

Estimation of Sparse MIMO Channels with Common Support

We consider the problem of estimating sparse communication channels in the MIMO context. In small to medium bandwidth communications, as in the current standards for OFDM and CDMA communication systems (with bandwidth up to 20 MHz), such channels are individually sparse and at the same time share a common support set. Since the underlying physical channels are inherently continuous-time, we propose a parametric sparse estimation technique based on finite rate of innovation (FRI) principles. Parametric estimation is especially relevant to MIMO communications as it allows for a robust estimation and concise description of the channels. The core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support. We show the application of our technique for channel estimation in OFDM (uniformly/contiguous DFT pilots) and CDMA downlink (Walsh-Hadamard coded schemes). In the presence of additive white Gaussian noise, theoretical lower bounds on the estimation of SCS channel parameters in Rayleigh fading conditions are derived. Finally, an analytical spatial channel model is derived, and simulations on this model in the OFDM setting show the symbol error rate (SER) is reduced by a factor 2 (0 dB of SNR) to 5 (high SNR) compared to standard non-parametric methods - e.g. lowpass interpolation.Comment: 12 pages / 7 figures. Submitted to IEEE Transactions on Communicatio

Deep Networks for Compressed Image Sensing

The compressed sensing (CS) theory has been successfully applied to image compression in the past few years as most image signals are sparse in a certain domain. Several CS reconstruction models have been recently proposed and obtained superior performance. However, there still exist two important challenges within the CS theory. The first one is how to design a sampling mechanism to achieve an optimal sampling efficiency, and the second one is how to perform the reconstruction to get the highest quality to achieve an optimal signal recovery. In this paper, we try to deal with these two problems with a deep network. First of all, we train a sampling matrix via the network training instead of using a traditional manually designed one, which is much appropriate for our deep network based reconstruct process. Then, we propose a deep network to recover the image, which imitates traditional compressed sensing reconstruction processes. Experimental results demonstrate that our deep networks based CS reconstruction method offers a very significant quality improvement compared against state of the art ones.Comment: This paper has been accepted by the IEEE International Conference on Multimedia and Expo (ICME) 201