EDITORIAL Open Access Editorial

Over the last three decades, there has been increasing interest in exploiting sparseness constraints in signal processing, that is, searching for target signals with as few non-zero entries as possible. This approach was, perhaps, first exploited in the modelling of excitation signals in speech processing or reflectivity sequences in seismic deconvolution with only a small number of non-zero values. Some 30 years later, the associated mathematical methods and application domains, both for singleand multiple-dimensional signals, have evolved to a point where sparse signal processing has become an area of study in its own right. This special issue on sparse signal processing, therefore, begins with a review article by Marvasti et al. [1], entitled A unified approach to sparse signal processing which provides a tutorial review of sparse signal recovery using various techniques with minimal sampling measurements, in effect, compressed sampling, and also describes applications of sparsity in a number of other challenging domains. Many of the articles in this special issue are related to applications of sparse signal processing. The next set of articles provides examples of where sparsity can be exploited in parameter estimation problems. The article by Djafari [2] uses a Bayesian inference approach to address both signal and image inversion problems wherein sparsity is considered either in the original or transformed signal space. Taxonomy of prior models is provided for the related probabilistic frameworks, and associated estimation algorithms are developed. Angelosante and Giannakis [3], in an invited article, consider the problem of estimating the parameters of timevarying autoregressive models. They overcome the lack of continuity and high computational complexity in working with high-dimensional datasets by casting their problem as a sparse regression with grouped variables. This is then solved with a group least-absolute shrinkage and selection operator, denoted Lasso. Numerical evaluations are employed to demonstrate the merits of the approach. Zhu et al [4]. also examine a parameter estimation problem in the context of Synthetic Aperture Radar (SAR). They address a difficult nonlinear problem by employing linearization and an over-complete dictionary. This is motivated by the sparse distribution in the observation space of SAR micromotion targets. A variational approximation framework is also exploited for Bayesian computation, and numerical simulations confirm the higher resolution achievable by the proposed approach over conventional methods. Xie et al. [5] provide a hybrid approach for 2D directionof-arrival estimation in the presence of mutual coupling across the array. They employ a manifold decomposition approach for the case when the number of sensors is sparse, smaller than required in traditional beamspacebased algorithms. In particular, an algorithm to estimate azimuth angle without exact knowledge of the mutual coupling is provided. Blanco and Nájar [6] propose an algorithm for estimating the angles of arrival of multiple uncorrelated sources impinging upon a uniform linear array. They use an overcomplete dictionary representation of the spatial covariance matrix model. A sparsity penalty is applied and a least angle regression/homotopic approach is used to solve the resulting objective function. Their approach is shown to achieve high resolution with the advantage of low computational cost. Li et al. [7] focus upon source localization with a single snapshot and improve the efficiency of an iterative adaptive approach by utilizing the optimal filter only on the spatial components corresponding to the impinging angles of the sources. Their evaluations confirm that this simplification attains comparable accuracy of source angle and power estimation with a substantial reduction in computational load. Sahnoun et al. [8] address multi-dimensional modal estimation using sparse estimation techniques in combination with an efficient multigrid approach. To overcome huge size in the necessary dictionaries, they refine their dictionaries over several levels of resolution. Their sparse modal * Correspondence: [email protected] Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran Full list of author information is available at the end of the article Marvasti et al. EURASIP Journal on Advances in Signal Processing 2012, 2012:90 http://asp.eurasipjournals.com/content/2012/1/90