Sharif Digital Repository

This letter proposes a dictionary learning algorithm for solving the grid mismatch problem in direction of arrival (DOA) estimation from both the array sensor data and from the sign of the array sensor data. Discretization of the grid in the sparsity-based DOA estimation algorithms is a problem, which leads to a bias error. To compensate this bias error, a dictionary learning technique is suggested, which is based on minimizing a suitable cost function. We also propose an algorithm for the estimation of DOA from the sign of the measurements. It extends the iterative method with adaptive thresholding algorithm to the 1-b compressed sensing framework. Simulation results show the effectiveness... 

This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted for visually enhanced quality of reconstruction of image signals. Although, the popular Mean Square Error (MSE) criterion is convex and simple, it may not be entirely consistent with Human Visual System (HVS). Thus, instead of ℓ2-norm or MSE, a new perceptual quality measure is used as the similarity criterion between the original and the reconstructed images. The proposed criterion called Convex SIMilarity (CSIM) index is a modified version of the Structural SIMilarity (SSIM) index, which despite its predecessor, is convex and uni-modal. We derive mathematical properties... 

This brief proposes a joint graph signal recovery and topology learning algorithm using a Variational Bayes (VB) framework in the case of non-Gaussian measurement noise. It is assumed that the graph signal is Gaussian Markov Random Field (GMRF) and the graph weights are considered statistical with the Gaussian prior. Moreover, the non-Gaussian noise is modeled using two distributions: Mixture of Gaussian (MoG), and Laplace. All the unknowns of the problem which are graph signal, Laplacian matrix, and the (Hyper)parameters are estimated by a VB framework. All the posteriors are calculated in closed forms and the iterative VB algorithm is devised to solve the problem. The efficiency of the... 

In this letter, the problem of non-coherent direction of arrival (DOA) estimation is investigated exploiting the sign of the measurements in order to resolve the inherent ambiguity of the problem. Although the phase values are inaccurate, the sign of real and imaginary parts of the measurements will most likely remain correct under limited phase errors. Furthermore, a new approach for solving the problem is proposed employing a modified version of the Majorization-Minimization (MM) technique, without any prior information about the number of incident signals. Some theoretical analyses of our proposed algorithm are also provided in the paper. Finally, the simulation results are presented,... 

In this paper, we suggest to use a steepest descent algorithm for learning a parametric dictionary in which the structure or atom functions are known in advance. The structure of the atoms allows us to find a steepest descent direction of parameters instead of the steepest descent direction of the dictionary itself. We also use a thresholded version of Smoothed- ℓ0 (SL0) algorithm for sparse representation step in our proposed method. Our simulation results show that using atom structure similar to the Gabor functions and learning the parameters of these Gabor-like atoms yield better representations of our noisy speech signal than non parametric dictionary learning methods like K-SVD, in... 

We propose an ℓ1 criterion for dictionary learning for sparse signal representation. Instead of directly searching for the dictionary vectors, our dictionary learning approach identifies vectors that are orthogonal to the subspaces in which the training data concentrate. We study conditions on the coefficients of training data that guarantee that ideal normal vectors deduced from the dictionary are local optima of the criterion. We illustrate the behavior of the criterion on a 2D example, showing that the local minima correspond to ideal normal vectors when the number of training data is sufficient. We conclude by describing an algorithm that can be used to optimize the criterion in higher... 

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 l1-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... 

This letter investigates the problem of sparse signal recovery in the presence of additive impulsive noise. The heavy-tailed impulsive noise is well modeled with stable distributions. Since there is no explicit formula for the probability density function of SαS distribution, alternative approximations are used, such as, generalized Gaussian distribution, which imposes ℓp-norm fidelity on the residual error. In this letter, we exploit a continuous mixed norm (CMN) for robust sparse recovery instead of ℓp-norm. We show that in blind conditions, i.e., in the case where the parameters of the noise distribution are unknown, incorporating CMN can lead to near-optimal recovery. We apply...