Dictionary Learning for Blind One Bit Compressed Sensing

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 \Ab and sparse domain matrix $\Phi$, \ie \Db=\Ab\Phi, 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 \Db. 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.Comment: 5 pages, 3 figure

Bayesian Hypothesis Testing for Block Sparse Signal Recovery

This letter presents a novel Block Bayesian Hypothesis Testing Algorithm (Block-BHTA) for reconstructing block sparse signals with unknown block structures. The Block-BHTA comprises the detection and recovery of the supports, and the estimation of the amplitudes of the block sparse signal. The support detection and recovery is performed using a Bayesian hypothesis testing. Then, based on the detected and reconstructed supports, the nonzero amplitudes are estimated by linear MMSE. The effectiveness of Block-BHTA is demonstrated by numerical experiments.Comment: 5 pages, 2 figures. arXiv admin note: text overlap with arXiv:1412.231

Proportionate Adaptive Graph Signal Recovery

This paper generalizes the proportionate-type adaptive algorithm to the graph signal processing and proposes two proportionate-type adaptive graph signal recovery algorithms. The gain matrix of the proportionate algorithm leads to faster convergence than least mean squares (LMS) algorithm. In this paper, the gain matrix is obtained in a closed-form by minimizing the gradient of the mean-square deviation (GMSD). The first algorithm is the Proportionate-type Graph LMS (Pt-GLMS) algorithm which simply uses a gain matrix in the recursion process of the LMS algorithm and accelerates the convergence of the Pt-GLMS algorithm compared to the LMS algorithm. The second algorithm is the Proportionate-type Graph Extended LMS (Pt-GELMS) algorithm, which uses the previous signal vectors alongside the signal of the current iteration. The Pt-GELMS algorithm utilizes two gain matrices to control the effect of the signal of the previous iterations. The stability analyses of the algorithms are also provided. Simulation results demonstrate the efficacy of the two proposed proportionate-type LMS algorithms

Block-sparse impulsive noise reduction in OFDM systems - a novel iterative bayesian approach

Using a novel block iterative Bayesian algorithm (Block-IBA), this paper presents a new impulsive noise reduction method for OFDM systems. The method utilizes the guard band null subcarriers and data subcarriers for the impulsive noise estimation and cancellation. Unlike some other general OFDM transceivers which use time-domain interleaving (TDI) to cancel impulsive noise, we design a specific receiver for bursty impulsive noise channels that removes the delay due to TDI and saves memory space. The Block-IBA first estimates the variance and the transition matrix of Markov chain model for the impulsive noise. It then iteratively estimates the amplitudes and positions of the block-sparse impulsive noise using the steepest-ascent based expectation-maximization (EM), and optimally selects the nonzero elements of the block-sparse impulsive noise by adaptive thresholding. Numerical experiments show that the proposed receiver outperforms existing receivers under the block-sparse impulsive noise environment