Abstract-We present a Bayesian approach for Sparse Component Analysis (SCA) in the noisy case. The algorithm is essentially a method for obtaining sufficiently sparse solutions of underdetermined systems of linear equations with additive Gaussian noise. In general, an underdetermined system of linear equations has infinitely many solutions. However, it has been shown that sufficiently sparse solutions can be uniquely identified. Our main objective is to find this unique solution. Our method is based on a novel estimation of source parameters and maximum a posteriori (MAP) estimation of sources. To tackle the great complexity of the MAP algorithm (when the number of sources and mixtures become large), we propose an Iterative Bayesian Algorithm (IBA). This IBA algorithm is based on the MAP estimation of sources, too, but optimized with a steepest-ascent method. The convergence analysis of the IBA algorithm and its convergence to true global maximum are also proved. Simulation results show that the performance achieved by the IBA algorithm is among the best, while its complexity is rather high in comparison to other algorithms. Simulation results also show the low sensitivity of the IBA algorithm to its simulation parameters.Index Terms-Atomic decomposition, blind source separation (BSS), sparse component analysis (SCA), sparse decomposition, sparse source separation.

This paper addresses the problem of scene reconstruction, incorporating wall-clutter mitigation, for compressed multi-view through-the-wall radar imaging. We consider the problem where the scene is sensed using different reduced sets of frequencies at different antennas. A joint Bayesian sparse recovery framework is first employed to estimate the antenna signal coefficients simultaneously, by exploiting the sparsity and correlations between antenna signals. Following joint signal coefficient estimation, a subspace projection technique is applied to segregate the target coefficients from the wall contributions. Furthermore, a multitask linear model is developed to relate the target coefficients to the scene, and a composite scene image is reconstructed by a joint Bayesian sparse framework, taking into account the interview dependencies. Experimental results show that the proposed approach improves reconstruction accuracy and produces a composite scene image in which the targets are enhanced and the background clutter is attenuated. ABSTRACT This paper addresses the problem of scene reconstruction, incorporating wall-clutter mitigation, for compressed multi-view through-the-wall radar imaging. We consider the problem where the scene is sensed using different reduced sets of frequencies at different antennas. A joint Bayesian sparse recovery framework is first employed to estimate the antenna signal coefficients simultaneously, by exploiting the sparsity and correlations between antenna signals. Following joint signal coefficient estimation, a subspace projection technique is applied to segregate the target coefficients from the wall contributions. Furthermore, a multitask linear model is developed to relate the target coefficients to the scene, and a composite scene image is reconstructed by a joint Bayesian sparse framework, taking into account the interview dependencies. Experimental results show that the proposed approach improves reconstruction accuracy and produces a composite scene image in which the targets are enhanced and the background clutter is attenuated. Index Terms-Multi-view through-the-wall radar imaging, wall clutter mitigation, compressed sensing, joint Bayesian sparse recovery.

Abstract-This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix A and sparse domain matrix Φ, i.e. D = AΦ, should be learned. Hence, we use dictionary learning to train this matrix. Towards that end, an appropriate continuous convex cost function is suggested for one bit compressed sensing and a simple steepest-descent method is exploited to learn the rows of the matrix D. Experimental results show the effectiveness of the proposed algorithm against the case of no dictionary learning, specially with increasing the number of training signals and the number of sign measurements.

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