AN L1 CRITERION FOR DICTIONARY LEARNING BY SUBSPACE IDENTIFICATION

Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under FET-Open grant number: 225913 (project SMALL).EPSRC Leadership Fellowship (EP/G007177/1

A novel underdetermined source recovery algorithm based on k-sparse component analysis

Sparse component analysis (SCA) is a popular method for addressing underdetermined blind source separation in array signal processing applications. We are motivated by problems that arise in the applications where the sources are densely sparse (i.e. the number of active sources is high and very close to the number of sensors). The separation performance of current underdetermined source recovery (USR) solutions, including the relaxation and greedy families, reduces with decreasing the mixing system dimension and increasing the sparsity level (k). In this paper, we present a k-SCA-based algorithm that is suitable for USR in low-dimensional mixing systems. Assuming the sources is at most (m−1) sparse where m is the number of mixtures; the proposed method is capable of recovering the sources from the mixtures given the mixing matrix using a subspace detection framework. Simulation results show that the proposed algorithm achieves better separation performance in k-SCA conditions compared to state-of-the-art USR algorithms such as basis pursuit, minimizing norm-L1, smoothed L0, focal underdetermined system solver and orthogonal matching pursuit

Frequency Estimation of Unbalanced Three-Phase Power System using a New LMS Algorithm

This paper presents a simple and easy implementable Least Mean Square (LMS) type approach for frequency estimation of three phase power system in an unbalanced condition. The proposed LMS type algorithm is based on a second order recursion for the complex voltage derived from Clarke's transformation which is proved in the paper. The proposed algorithm is real adaptive filter with real parameter (not complex) which can be efficiently implemented by DSP. In unbalanced situations, simulation experiments show the advantages and drawbacks of the proposed algorithm in comparison to Complex LMS (CLMS) and Augmented Complex LMS (ACLMS) method

COMPRESSED SENSING BLOCK MAP-LMS ADAPTIVE FILTER FOR SPARSE CHANNEL ESTIMATION AND A BAYESIAN CRAMER-RAO BOUND

This paper suggests to use a Block MAP-LMS (BMAP-LMS) adaptive filter instead of an Adaptive Filter called MAP-LMS for estimating the sparse channels. Moreover to faster convergence than MAP-LMS, this block-based adaptive filter enables us to use a compressed sensing version of it which exploits the sparsity of the channel outputs to reduce the sampling rate of the received signal and to alleviate the complexity of the BMAP-LMS. Our simulations show that our proposed algorithm has faster convergence and less final MSE than MAP-LMS, while it is more complex than MAP-LMS. Moreover, some lower bounds for sparse channel estimation is discussed. Specially, a Cramer-Rao bound and a Bayesian Cramer-Rao bound is also calculated. 1

ESTIMATING THE MIXING MATRIX IN SPARSE COMPONENT ANALYSIS (SCA) USING EM ALGORITHM AND ITERATIVE BAYESIAN CLUSTERING

In this paper, we focus on the mixing matrix estimation which is the first step of Sparse Component Analysis. We propose a novel algorithm based on Expectation-Maximization (EM) algorithm in the case of two-sensor set up. Then, a novel iterative Bayesian clustering is applied to yield better results in estimating the mixing matrix. Also, we compute the Maximum Likelihood (ML) estimates of the elements of the second row of the mixing matrix based on each cluster. The simulations show that the proposed method has better accuracy and less failure than the EM-Laplacian Mixture Model (EM-LMM) method. 1

An iterative Bayesian algorithm for block-sparse signal reconstruction

This paper presents a novel iterative Bayesian algorithm, Block Iterative Bayesian Algorithm (Block-IBA), for reconstructing block-sparse signals with unknown block structures. Unlike the other existing algorithms for block sparse signal recovery which assume the cluster structure of the non-zero elements of the unknown signal to be independent and identically distributed (i.i.d.), we use a more realistic Bernoulli-Gaussian hidden Markov model (BGHMM) to capture the burstiness (block structure) of the impulsive noise in practical applications such as Power Line Communication (PLC). The Block-IBA iteratively estimates the amplitudes and positions of the block-sparse signal based on Expectation-Maximization (EM) algorithm which is also optimized with the steepest-ascent method. Simulation results show the effectiveness of our algorithm for block-sparse signal recovery