In the last decade, there has been a great interest in finding new priors for Blind Source Separation (BSS). Some of the most interesting of them are sparsity, non-negativity and boundedness of the sources, since they consist in weaker assumptions when compared to the classical statistical independence hypothesis. In this paper, we propose a new criterion for Bounded Component Analysis (BCA), using the $\ell_\infty$ norm, with an associated algorithm based on Givens Rotations. We analyze our proposal and evaluate it with numerical simulations for three kinds of bounded signals. From both theoretical and experimental results we show that the $\ell_\infty$ norm is a suitable contrast function for BCA, presenting very good results when compared to the state-of-the-art algorithm.

In this paper we present three new algorithms for sparse multichannel blind deconvolution. The first algorithm is based on a cascade of a forward and a backward prediction error filter. The second consists in an alternating minimization algorithm for estimating both the reflectivity series and the seismic wavelet. The last one is a regularized version of the so called Euclid deconvolution, solved by the well known fast iterative shrinkage-thresholding algorithm (FISTA). Simulation results illustrate that the three algorithms presents some quite interesting results in both synthetic and real data.

In this paper we present a new criterion for bounded component analysis, a quite new approach for the Blind Source Separation problem. For the determined case, we show that the ‘1-norm of the estimated sources can be used as a contrast for the problem. We present a blind algorithm for the source separation of independents sources or mixtures of correlated sources by only a rotation matrix. We also present a variety of simulations assessing the performance of the proposed approach.

This letter introduces the concept of antisparse Blind Source Separation (BSS), proposing a suitable criterion based on the $\ell_\infty$ norm to explore the antisparsity feature. The effectiveness of the criterion is theoretically demonstrated and it is also evaluated by computational simulations, which consider up to ten distinct sources with different correlation levels. Moreover, we simulated a scenario in wireless communication with binary sources, comparing our approach to the Constant Modulus algorithm. Both the theoretical and the simulation results highlight the potentiality of using antisparsity as a prior in BSS.