Related papers: Efficient atom selection strategy for iterative sp…
Sparse coding is a class of unsupervised methods for learning a sparse representation of the input data in the form of a linear combination of a dictionary and a sparse code. This learning framework has led to state-of-the-art results in…
In dictionary selection, several atoms are selected from finite candidates that successfully approximate given data points in the sparse representation. We propose a novel efficient greedy algorithm for dictionary selection. Not only does…
In this paper, we propose a Bayesian Hypothesis Testing Algorithm (BHTA) for sparse representation. It uses the Bayesian framework to determine active atoms in sparse representation of a signal. The Bayesian hypothesis testing based on…
Sparse recovery algorithms are of utmost importance for estimation processes in wireless communications. However, communication systems such as massive multiple input multiple output (MIMO) systems are rapidly growing in dimension, which…
Sparse signal representations based on linear combinations of learned atoms have been used to obtain state-of-the-art results in several practical signal processing applications. Approximation methods are needed to process high-dimensional…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…
In this paper, we improve iterative greedy search algorithms in which atoms are selected serially over iterations, i.e., one-by-one over iterations. For serial atom selection, we devise two new schemes to select an atom from a set of…
Sparse representation-based classifiers have shown outstanding accuracy and robustness in image classification tasks even with the presence of intense noise and occlusion. However, it has been discovered that the performance degrades…
Proportionate type algorithms were developed and excessively used in the echo cancellation problems due to sparse characteristics of the echo channels. In the past, most of the attention was paid to a particular type of proportionate…
A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation…
A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes…
We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…
We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…
Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…
In this work we propose a nonconvex two-stage \underline{s}tochastic \underline{a}lternating \underline{m}inimizing (SAM) method for sparse phase retrieval. The proposed algorithm is guaranteed to have an exact recovery from $O(s\log n)$…