Sparse representations have been extended to deal with color images composed of three channels. A review of dictionary-learning-based sparse representations for color images is made here, detailing the differences between the models, and comparing their results on the real and simulated data. These models are considered in a unifying framework that is based on the degrees of freedom of the linear filtering/transformation of the color channels. Moreover, this allows it to be shown that the scalar quaternionic linear model is equivalent to constrained matrix-based color filtering, which highlights the filtering implicitly applied through this model. Based on this reformulation, the new color filtering model is introduced, using unconstrained filters. In this model, spatial morphologies of color images are encoded by atoms, and colors are encoded by color filters. Color variability is no longer captured in increasing the dictionary size, but with color filters, this gives an efficient color representation.

Blind source separation (BSS) is a very popular technique to analyze data which can be modeled as linear mixtures of elementary sources. Standard approaches generally make the assumption that such sources are statistically independent or at least uncorrelated. However, this is barely the case for real-world sources which are very often partially correlated. We present a new sparsity-enforcing BSS method coined Adaptive Morphological Component Analysis (AMCA) designed to retrieve sparse and partially correlated sources based on an adaptive weighting scheme. Numerical experiments have been carried out which show that the proposed method is robust to the partial correlation of the sources while standard BSS techniques fail. The performances of the proposed algorithm are further illustrated with simulations in the context of astrophysics.

Nonnegative blind source separation, which is also referred to as nonnegative matrix factorization (NMF), is a very active field in domains as different as astrophysics, audio processing, and biomedical signal processing. In this context, the efficient retrieval of the sources requires the use of signal priors such as sparsity. Although NMF has been well studied with sparse constraints in the direct domain, only very few algorithms can encompass nonnegativity together with sparsity in a transformed domain since simultaneously dealing with two priors in two different domains is challenging. In this paper, we show how a sparse NMF algorithm called nonnegative generalized morphological component analysis (nGMCA) can be extended to impose nonnegativity in the direct domain along with sparsity in a transformed domain, with both analysis and synthesis formulations. To the best of our knowledge, this work presents the first comparison of analysis and synthesis priors---as well as their reweighted versions---in the context of blind source separation. Comparisons with state-of-the-art NMF algorithms on realistic data show the efficiency as well as the robustness of the proposed algorithms.

In this letter, a review of the quaternionic least mean squares (QLMS) algorithm is proposed. Three versions coming from three derivation ways exist: the original QLMS [1] based on componentwise gradients, HR-QLMS [2] based on a quaternion gradient operator and iQLMS [3] based on an involutions-gradient. Noting and investigating the differences between the three QLMS formulations, we show that the original QLMS suffers from a mistake in the derivation calculus. Thus, we propose to derive rigorously the criterion following the first way, giving the correct version of QLMS. A comparison with the other QLMS versions validates these results on simulated data.

In this paper, a novel gas identification approach based on the Recursive Least Squares (RLS) algorithm is proposed. We detail some adaptations of RLS to be applied to a sensor matrix of several technologies in optimal conditions. The low complexity of the algorithm and its ability to process online samples from multi-sensor make the real-time identification of volatile compounds possible. The effectiveness of this approach to early detect and recognize explosive compounds in the air has been successfully demonstrated on an experimentally obtained dataset.