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In this paper we present an algorithm for complex-valued sparse representation. In our previous work we presented an algorithm for Sparse representation based on smoothed l0-norm. Here we extend that algorithm to complex-valued signals. The proposed algorithm is compared to FOCUSS algorithm and it is experimentally shown that the proposed algorithm is about two or three orders of magnitude faster than FOCUSS while providing approximately the same accuracy. ©2008 IEEE  

In this paper, a new algorithm for Sparse Component Analysis (SCA) or atomic decomposition on over-complete dictionaries is presented. The algorithm is essentially a method for obtaining sufficiently sparse solutions of underdetermined systems of linear equations. The solution obtained by the proposed algorithm is compared with the minimum ℓ1-norm solution achieved by Linear Programming (LP). It is experimentally shown that the proposed algorithm is about two orders of magnitude faster than the state-of-the-art ℓ1-magic, while providing the same (or better) accuracy. © Springer-Verlag Berlin Heidelberg 2007  

We propose a new method for estimating the mixing matrix, A, in the linear model x(t) = As(t),t = 1,...,T, for the problem of underdetermined Sparse Component Analysis (SCA). Contrary to most previous algorithms, there can be more than one dominant source at each instant (we call it a "multiple dominant" problem). The main idea is to convert the multiple dominant problem to a series of single dominant problems, which may be solved by well-known methods. Each of these single dominant problems results in the determination of some columns of A. This results in a huge decrease in computations, which lets us to solve higher dimension problems that were not possible before. © Springer-Verlag... 

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... 

In this paper, we suggest to use a modified version of Smoothed- ℓ0 (SL0) algorithm in the sparse representation step of iterative dictionary learning algorithms. In addition, we use a steepest descent for updating the non unit columnnorm dictionary instead of unit column-norm dictionary. Moreover, to do the dictionary learning task more blindly, we estimate the average number of active atoms in the sparse representation of the training signals, while previous algorithms assumed that it is known in advance. Our simulation results show the advantages of our method over K-SVD in terms of complexity and performance. ©2009 IEEE  

Sparse Decomposition (SD) of a signal on an overcomplete dictionary has recently attracted a lot of interest in signal processing and statistics, because of its potential application in many different areas including Compressive Sensing (CS). However, in the current literature, the dictionary matrix has generally been assumed to be of full-rank. In this paper, we consider non-full-rank dictionaries (which are not even necessarily overcomplete), and extend the definition of SD over these dictionaries. Moreover, we present an approach which enables to use previously developed SD algorithms for this non-full-rank case. Besides this general approach, for the special case of the Smoothed ℓ0 (SL0)... 

One of the major problems in underdetermined Sparse Component Analysis (SCA) is the appropriate estimation of the mixing matrix, A, in the linear model x(t) = As(t), especially where more than one source is active at each instant of time (It is called 'multiple dominant problem'). Most of the previous algorithms were restricted to single dominant problem in which it is assumed that at each instant, there is at most one single dominant component. Moreover, because of high computational load, all present methods for multiple dominant problem are practical only for small scale cases (By 'small scale' we mean that the average number of active sources at each instant, k, is less than 5). In this... 

One of the major problems in underdetermined Sparse Component Analysis (SCA) in the field of (semi) Blind Source Separation (BSS) is the appropriate estimation of the mixing matrix, A, in the linear model X = AS, especially where more than one source is active at each instant of time. Most existing algorithms require the restriction that at each instant (i.e. in each column of the source matrix S), there is at most one single dominant component. Moreover, these algorithms require that the number of sources must be determined in advance. In this paper, we proposed a new algorithm for estimating the matrix A, which does not require the restriction of single dominant source at each instant.... 

In this paper, we focus on the mixing matrix estimation which is the first step of Sparse Component Analysis. We propose a novel algorithm based on Expectation- Maximization (EM) algorithm in the case of two-sensor set up. Then, a novel iterative Bayesian clustering is applied to yield better results in estimating the mixing matrix. Also, we compute the Maximum Likelihood (ML) estimates of the elements of the second row of the mixing matrix based on each cluster. The simulations show that the proposed method has better accuracy and less failure than the EM-Laplacian Mixture Model (EM-LMM) method. copyright by EURASIP  

In this paper we propose a new method for estimating the mixing matrix, A, in the linear model X = AS, for the problem of underdetermined Sparse Component Analysis (SCA). Contrary to most existing algorithms, in the proposed algorithm there may be more than one active source at each instant (i.e. in each column of the source matrix S), and the number of sources is not required to be known in advance. Since in the cases where more than one source is active at each instant, data samples concentrate around multidimensional subspaces, the idea of our method is to first estimate these subspaces and then estimate the mixing matrix from these estimated subspaces. ©2007 IEEE  

In this paper, a new algorithm for Sparse Component Analysis (SCA) in the noisy underdetermined case (i.e., with more sources than sensors) is presented. The solution obtained by the proposed algorithm is compared to the minimum l1 -norm solution achieved by Linear Programming (LP). Simulation results show that the proposed algorithm is approximately 10 dB better than the LP method with respect to the quality of the estimated sources. It is due to optimality of our solution (in the MAP sense) for source recovery in noisy underdetermined sparse component analysis in the case of spiky model for sparse sources and Gaussian noise. © 2007 IEEE  

This paper is a survey of semi-blind source separation approaches. Since Gaussian iid signals are not separable, simplest priors suggest to assume non Gaussian iid signals, or Gaussian non iid signals. Other priors can also been used, for instance discrete or bounded sources, positivity, etc. Although providing a generic framework for semi-blind source separation, Sparse Component Analysis and Bayesian ICA will just sketched in this paper, since two other survey papers develop in depth these approaches. © 2006 i6doc.com publication. All rights reserved  

In this paper, we address theoretical limitations in estimating the mixing matrix in noisy Sparse Component Analysis (SCA) in the two-sensor case. We obtain the Cramér-Rao Bound (CRB) error estimation of the mixing matrix based on the observation vector x=(x1,x2)T. Using the Bernoulli-Gaussian (BG) sparse distribution for sources, and some reasonable approximations, the Fisher Information Matrix (FIM) is approximated by a diagonal matrix. Then, the effect of off-diagonal terms in computing the CRB is investigated. Moreover, we compute an oracle CRB versus the blind uniform CRB and show that this is only 3 dB better than the blind uniform CRB. Finally, the CRB, the approximated CRB, the... 

Let A be an n × m matrix with m > n, and suppose that the underdetermined linear system As = x admits a sparse solution ∥s 0∥o < 1/2spark(A). Such a sparse solution is unique due to a well-known uniqueness theorem. Suppose now that we have somehow a solution ŝ as an estimation of s0, and suppose that ŝ is only "approximately sparse", that is, many of its components are very small and nearly zero, but not mathematically equal to zero. Is such a solution necessarily close to the true sparsest solution? More generally, is it possible to construct an upper bound on the estimation error ∥ŝ - s 0∥2 without knowing s0? The answer is positive, and in this paper, we construct such a bound based on... 

In this paper, we propose a Bayesian Pursuit algorithm for sparse representation. It uses both the simplicity of the pursuit algorithms and optimal Bayesian framework to determine active atoms in sparse representation of a signal. We show that using Bayesian Hypothesis testing to determine the active atoms from the correlations leads to an efficient activity measure. Simulation results show that our suggested algorithm has better performance among the algorithms which have been implemented in our simulations in most of the cases. ©2009 IEEE