Sharif Digital Repository

A dictionary learning algorithm learns a set of atoms from some training signals in such a way that each signal can be approximated as a linear combination of only a few atoms. Most dictionary learning algorithms use a two-stage iterative procedure. The first stage is to sparsely approximate the training signals over the current dictionary. The second stage is the update of the dictionary. In this paper we develop some atom-by-atom dictionary learning algorithms, which update the atoms sequentially. Specifically, we propose an efficient alternative to the well-known K-SVD algorithm, and show by various experiments that the proposed algorithm is much faster than K-SVD while its results are... 

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... 

In this paper we propose a fast and efficient algorithm for learning overcomplete dictionaries. The proposed algorithm is indeed an alternative to the well-known K-Singular Value Decomposition (K-SVD) algorithm. The main drawback of K-SVD is its high computational load especially in high-dimensional problems. This is due to the fact that in the dictionary update stage of this algorithm an SVD is performed to update each column of the dictionary. Our proposed algorithm avoids performing SVD and instead uses a special form of alternating minimization. In this way, as our simulations on both synthetic and real data show, our algorithm outperforms K-SVD in both computational load and the quality... 

This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications that work with multiple signals maintaining some degree of dependency, e.g., radar and sensor networks. We introduce a new method towards joint recovery of several independent sparse signals with the same support. We provide an analytical discussion of the convergence of our method, called Simultaneous Iterative Method (SIM). In this study, we compared our method with other group-sparse reconstruction techniques, namely Simultaneous Orthogonal Matching Pursuit (SOMP) and Block Iterative Method with Adaptive Thresholding (BIMAT), through numerical experiments. The simulation... 

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... 

Orthogonal Matching Pursuit is an iterative greedy algorithm used to find a sparse approximation for high-dimensional signals. The algorithm is most popularly used in Compressive Sensing, which allows for the reconstruction of sparse signals at rates lower than the Shannon-Nyquist frequency, which has traditionally been used in a number of applications such as MRI and computer vision and is increasingly finding its way into Big Data and data center analytics. OMP traditionally suffers from being computationally intensive and time-consuming, this is particularly a problem in the area of Big Data where the demand for computational resources continues to grow. In this paper, the data-level... 

This paper presents efficient algorithms for learning low-coherence dictionaries. First, a new algorithm based on proximal methods is proposed to solve the dictionary learning (DL) problem regularized with the mutual coherence of dictionary. This is unlike the previous approaches that solve a regularized problem where an approximate incoherence promoting term, instead of the mutual coherence, is used to encourage low-coherency. Then, a new solver is proposed for constrained low-coherence DL problem, i.e., a DL problem with an explicit constraint on the mutual coherence of the dictionary. As opposed to current methods, which follow a suboptimal two-step approach, the new algorithm directly...