Traditional speech enhancement (SE) algorithms usually have fluctuant performance when they deal with different types of noisy speech signals. In this paper, we propose multi-task Bayesian compressive sensing based speech enhancement (MT-BCS-SE) algorithm to achieve not only comparable performance to but also more stable performance than traditional SE algorithms. MT-BCS-SE algorithm utilizes the dependence information among compressive sensing (CS) measurements and the sparsity of speech signals to perform SE. To obtain sufficient sparsity of speech signals, we adopt overcomplete dictionary to transform speech signals into sparse representations. K-SVD algorithm is employed to learn various overcomplete dictionaries. The influence of the overcomplete dictionary on MT-BCS-SE algorithm is evaluated through large numbers of experiments, so that the most suitable dictionary could be adopted by MT-BCS-SE algorithm for obtaining the best performance. Experiments were conducted on well-known NOIZEUS corpus to evaluate the performance of the proposed algorithm. In these cases of NOIZEUS corpus, MT-BCS-SE is shown that to be competitive or even superior to traditional SE algorithms, such as optimally-modified log-spectral amplitude (OMLSA), multi-band spectral subtraction (SSMul), and minimum mean square error (MMSE), in terms of signal-noise ratio (SNR), speech enhancement gain (SEG) and perceptual evaluation of speech quality (PESQ) and to have better stability than traditional SE algorithms.

This paper presents a method for learning an overcomplete, nonnegative dictionary and for obtaining the corresponding coefficients so that a group of nonnegative signals can be sparsely represented by them. This is accomplished by posing the learning as a problem of nonnegative matrix factorization (NMF) with maximization of the incoherence of the dictionary and of the sparsity of coefficients. By incorporating a dictionary-incoherence penalty and a sparsity penalty in the NMF formulation and then adopting a hierarchically alternating optimization strategy, we show that the problem can be cast as two sequential optimal problems of quadratic functions. Each optimal problem can be solved explicitly so that the whole problem can be efficiently solved, which leads to the proposed algorithm, i.e., sparse hierarchical alternating least squares (SHALS). The SHALS algorithm is structured by iteratively solving the two optimal problems, corresponding to the learning process of the dictionary and to the estimating process of the coefficients for reconstructing the signals. Numerical experiments demonstrate that the new algorithm performs better than the nonnegative K-SVD (NN-KSVD) algorithm and several other famous algorithms, and its computational cost is remarkably lower than the compared algorithms.

An unsupervised algorithm is proposed for learning overcomplete topographic representations of nature image. Our method is based on Independent Component Analysis (ICA) model due to its superiority on feature extraction, and overcomes the weakness of traditional method in fast overcomplete learning. Besides, the learnt topographic representation, resembling receptive fields of complex cells, can be used as descriptors to extract invariant features. Recognition experiments on Caltech-101 dataset confirm that these complex cell descriptors are not only efficient in feature extraction but achieve comparable performances to traditional descriptors.

The purpose of this study is to show a class of near shift-invariant and orientation-selective transform based on even-stacked cosine-modulated filter banks (ECFBs) which originally have been proposed by Lin and Vaidyanathan. It is well-known that ECFBs can be designed by the modulation of just one prototype filter and guarantee the linear phase property. We extend this class to delay-less oversampled ECFB and show two additional attractive features; high directional selectivity and near shift-invariant property. In this paper, these properties are verified by theoretical analysis and demonstrations.

In this letter, we learned overcomplete filters to model rich priors of nature images. Our approach extends the Gaussian Scale Mixture Fields of Experts (GSM FOE), which is a fast approximate model based on Fields of Experts (FOE). In these previous image prior model, the overcomplete case is not considered because of the heavy computation. We introduce the assumption of quasi-orthogonality to the GSM FOE, which allows us to learn overcomplete filters of nature images fast and efficiently. Simulations show these obtained overcomplete filters have properties similar with those of Fields of Experts', and denoising experiments also show the superiority of our model.

We propose a blind source separation algorithm for the mixture of finite alphabet sources where sensors are less than sources. The algorithm consists of an update equation of an estimated mixing matrix and enumeration of the inferred sources. We present the bound of a step size for the stability of the algorithm and two methods of assignment of the initial point of the estimated mixing matrix. Simulation results verify the proposed algorithm.