Blind source separation (BSS) methods are useful tools to recover or enhance individual speech sources from their mixtures in a multi-talker environment. A class of efficient BSS methods are based on the mutual exclusion hypothesis of the source signal Fourier spectra on the timefrequency (TF) domain, and subsequent data clustering and classification. Though such methodology is simple, the discontinuous decisions in the TF domain for classification often cause defects in the recovered signals in the time domain. The defects are perceived as unpleasant ringing sounds, the so called musical noise. Post-processing is desired for further quality enhancement. In this paper, an efficient musical noise reduction method is presented based on a convex model of time-domain sparse filters. The sparse filters are intended to cancel out the interference due to major sparse peaks in the mixing coefficients or physically the early arrival and high energy portion of the room impulse responses. This strategy is efficiently carried out by l1 regularization and the split Bregman method. Evaluations by both synthetic and room recorded speech and music data show that our method outperforms existing musical noise reduction methods in terms of objective and subjective measures. Our method can be used as a post-processing tool for more general and recent versions of TF domain BSS methods as well.

Face tracking is an important computer vision technology that has been widely adopted in many areas, from cell phone applications to industry robots. In this paper, we introduce a novel way to parallelize a face contour detecting application based on the color-entropy preprocessed ChanVese model utilizing a total variation G-norm. This particular application is a complicated and unsupervised computational method requiring a large amount of calculations. Several core parts therein are difficult to parallelize due to heavily correlated data processing among iterations and pixels.

We study the enhanced diffusivity in the so called elephant random walk model with stops (ERWS) by including symmetric random walk steps at small probability \epsilon . At any \epsilon , the large time behavior transitions from sub-diffusive at \epsilon to diffusive in a wedge shaped parameter regime where the diffusivity is strictly above that in the un-perturbed ERWS model in the \epsilon limit. The perturbed ERWS model is shown to be solvable with the first two moments and their asymptotics calculated exactly in both one and two space dimensions. The model provides a discrete analytical setting of the residual diffusion phenomenon known for the passive scalar transport in chaotic flows (eg generated by time periodic cellular flows and statistically sub-diffusive) as molecular diffusivity tends to zero.

In this paper, we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition, we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual diffusion refers to the nonzero effective (homogenized) diffusion in the limit of zero molecular diffusion as a result of chaotic mixing of the streamlines. In this limit, traditional numerical methods typically fail since the solutions of the advection-diffusion equations develop sharp gradients. Instead of solving the Fokker--Planck equation in the Eulerian formulation, we compute the motion of particles in the Lagrangian formulation, which is modeled by stochastic differential equations (SDEs). We propose an effective numerical integrator based on a splitting method to solve the corresponding SDEs in which the deterministic subproblem is symplectic preserving while the random subproblem

Speech signals are often produced or received in the presence of noise, which is known to degrade the performance of a speech recognition system. In this paper, a perception-and PDE-based nonlinear transformation was developed to process spoken words in noisy environment. Our goal is to distinguish essential speech features and suppress noise so that the processed words are better recognized by a computer software. The nonlinear transformation was made on the spectrogram (short-term Fourier spectra) of speech signals, which reveals the signal energy distribution in time and frequency. The transformation reduces noise through time adaptation (reducing temporally slowly varying portions of spectra) and enhances spectral peaks (formants) by evolving a focusing quadratic fourth-order PDE. Short-term spectra of speech signals were initially divided into three (low, mid and high) frequency bands based