Dictionary Learning for Blind One Bit Compressed Sensing

This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix \Ab and sparse domain matrix $\Phi$, \ie \Db=\Ab\Phi, should be learned. Hence, we use dictionary learning to train this matrix. Towards that end, an appropriate continuous convex cost function is suggested for one bit compressed sensing and a simple steepest-descent method is exploited to learn the rows of the matrix \Db. Experimental results show the effectiveness of the proposed algorithm against the case of no dictionary learning, specially with increasing the number of training signals and the number of sign measurements.Comment: 5 pages, 3 figure

Recovery of Missing Samples Using Sparse Approximation via a Convex Similarity Measure

In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of image signal. This problem is also known as inpainting in the context of image processing and for this purpose, we suggest an iterative sparse recovery algorithm based on constrained $l_1$-norm minimization with a new fidelity metric. The proposed metric called Convex SIMilarity (CSIM) index, is a simplified version of the Structural SIMilarity (SSIM) index, which is convex and error-sensitive. The optimization problem incorporating this criterion, is then solved via Alternating Direction Method of Multipliers (ADMM). Simulation results show the efficiency of the proposed method for missing sample recovery of 1D patch vectors and inpainting of 2D image signals

Bayesian Hypothesis Testing for Block Sparse Signal Recovery

This letter presents a novel Block Bayesian Hypothesis Testing Algorithm (Block-BHTA) for reconstructing block sparse signals with unknown block structures. The Block-BHTA comprises the detection and recovery of the supports, and the estimation of the amplitudes of the block sparse signal. The support detection and recovery is performed using a Bayesian hypothesis testing. Then, based on the detected and reconstructed supports, the nonzero amplitudes are estimated by linear MMSE. The effectiveness of Block-BHTA is demonstrated by numerical experiments.Comment: 5 pages, 2 figures. arXiv admin note: text overlap with arXiv:1412.231

Distributed Unmixing of Hyperspectral Data With Sparsity Constraint

Spectral unmixing (SU) is a data processing problem in hyperspectral remote sensing. The significant challenge in the SU problem is how to identify endmembers and their weights, accurately. For estimation of signature and fractional abundance matrices in a blind problem, nonnegative matrix factorization (NMF) and its developments are used widely in the SU problem. One of the constraints which was added to NMF is sparsity constraint that was regularized by L 1/2 norm. In this paper, a new algorithm based on distributed optimization has been used for spectral unmixing. In the proposed algorithm, a network including single-node clusters has been employed. Each pixel in hyperspectral images considered as a node in this network. The distributed unmixing with sparsity constraint has been optimized with diffusion LMS strategy, and then the update equations for fractional abundance and signature matrices are obtained. Simulation results based on defined performance metrics, illustrate advantage of the proposed algorithm in spectral unmixing of hyperspectral data compared with other methods. The results show that the AAD and SAD of the proposed approach are improved respectively about 6 and 27 percent toward distributed unmixing in SNR=25dB.Comment: 6 pages, conference pape