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A new algorithm for learning jointly reconstructive and discriminative dictionaries for sparse representation (SR) is presented. While in a usual dictionary learning algorithm like K-SVD only the reconstructive aspect of the sparse representations is considered to learn a dictionary, in our proposed algorithm, which we call K-LDA, the discriminative aspect of the sparse representations is also addressed. In fact, K-LDA is an extension of K-SVD in the case that the class informations (labels) of the training data are also available. K-LDA takes into account these information in order to make the sparse representations more discriminate. It makes a trade-off between the amount of... 

Dictionary learning (DL) for sparse representation has been widely investigated during the last decade. A DL algorithm uses a training data set to learn a set of basis functions over which all training signals can be sparsely represented. In practice, training signals may contain a few outlier data, whose structures differ from those of the clean training set. The presence of these unpleasant data may heavily affect the learning performance of a DL algorithm. In this paper we propose a robust-to-outlier formulation of the DL problem. We then present an algorithm for solving the resulting problem. Experimental results on both synthetic data and image denoising demonstrate the promising... 

In this paper we address the problem of image interpolation using Gaussian Mixture Models (GMM) as a prior. Previous methods of image restoration with GMM have not considered spatial (geometric) distance between patches in clustering, failing to fully exploit the coherency of nearby patches. The GMM framework in our method for image interpolation is based on the assumption that the accumulation of similar patches in a neighborhood are derived from a multivariate Gaussian probability distribution with a specific covariance and mean. An Expectation Maximization-like (EM-like) algorithm is used in order to determine patches in a cluster and restore them. The results show that our image... 

Blind Source Separation (BSS) is the problem of separating signals which are mixed through an unknown function from a number of observations, without any information about the mixing model. Although it has been mathematically proven that the separation can be done when the mixture is linear, there is not any proof for the separability of nonlinearly mixed signals. Our contribution in this paper is performing nonlinear BSS for sparse sources. It is shown in this case, sources are separable even if the problem is under-determined (the number of observations is less than the number of source signals). However in the most general case (when the nonlinear mixing model can be of any kind and there... 

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, an algorithm for image coding based on a sparse 3-dimensional Discrete Cosine Transform (3D DCT) is studied. The algorithm is essentially a method for achieving a sufficiently sparse representation using 3D DCT. The experimental results obtained by the algorithm are compared to the 2D DCT (used in JPEG standard) and wavelet db9/7 (used in JPEG2000 standard). It is experimentally shown that the algorithm, that only uses DCT but in 3 dimensions, outperforms the DCT used in JPEG standard and achieves comparable results (but still less than) the wavelet transform. © Springer-Verlag Berlin Heidelberg 2009  

The problem of removing white zero-mean Gaussian noise from an image is an interesting inverse problem to be investigated in this paper through sparse and redundant representations. However, finding the sparsest possible solution in the noise scenario was of great debate among the researchers. In this paper we make use of new approach to solve this problem and show that it is comparable with the state-of-art denoising approaches. © Springer-Verlag Berlin Heidelberg 2009  

In this paper, a proof is provided to show that Gaussian signals will lose their Gaussianity if they are passed through a polynomial of an order greater than 1. This can help in blind compensation of polynomial nonlinearities on Gaussian sources by forcing the output to follow a Gaussian distribution (the term 'blind' refers to lack of any prior information about the nonlinear function). It may have many applications in different fields of nonlinear signal processing for removing the nonlinearity. Particularly, in nonlinear blind source separation, it can be used as a pre-processing step to transform the problem to a linear one, which is already well studied in the literature. This idea is... 

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... 

Permutation and scaling ambiguities are relevant issues in tensor decomposition and source separation algorithms. Although these ambiguities are inevitable when working on real data sets, it is preferred to eliminate these uncertainties for evaluating algorithms on synthetic data sets. As shown in the paper, the existing performance indices for this purpose are either greedy and unreliable or computationally costly. In this paper, we propose a new performance index, called CorrIndex, whose reliability can be proved theoretically. Moreover, compared to previous performance indices, it has a low computational cost. Theoretical results and computer experiments demonstrate these advantages of... 

In this paper, we address the problem of dictionary learning for sparse representation. Considering the regularized form of the dictionary learning problem, we propose a method based on a homotopy approach, in which the regularization parameter is overall decreased along iterations. We estimate the value of the regularization parameter adaptively at each iteration based on the current value of the dictionary and the sparse coefficients, such that it preserves both sparse coefficients and dictionary optimality conditions. This value is, then, gradually decreased for the next iteration to follow a homotopy method. The results show that our method has faster implementation compared to recent... 

This paper studies denoising of images contaminated with additive white Gaussian noise (AWGN). In recent years, clustering-based methods have shown promising performances. In this paper we show that low-rank subspace clustering provides a suitable clustering problem that minimizes the lower bound on the MSE of the denoising, which is optimum for Gaussian noise. Solving the corresponding clustering problem is not easy. We study some global and local sub-optimal solutions already presented in the literature and show that those that solve a better approximation of our problem result in better performances. A simple image denoising method based on dictionary learning using the idea of...