In this paper, we analyze the Bregman iterative model using the G-norm. Firstly, we show the convergence of the iterative model. Secondly, using the source condition and the symmetric Bregman distance, we consider the error estimations between the iterates and the exact image both in the case of clean and noisy data. The results show that the Bregman iterative model using the G-norm has the similar good properties as the Bregman iterative model using the L2-norm.

Numerical homogenization and multiscale finite element methods construct effective properties on a coarse grid by solving local problems and extracting the average effective properties from these local solutions. In some cases, the solutions of local problems can be expensive to compute due to scale disparity. In this setting, one can basically apply a homogenization or multiscale method reiteratively to solve for the local problems. This process is known as reiterated homogenization and has many variations in the numerical context. Though the process seems to be a straightforward extension of two-level process, it requires some careful implementation and the concept development for problems without scale separation and high contrast. In this paper, we consider the generalized multiscale finite element method (GMsFEM) and apply it iteratively to construct its multiscale basis functions. The main idea of the

In this paper, we analyze the uniqueness of the sparse time frequency decomposition and investigate the eciency of the nonlinear matching pursuit method. Under the assumption of scale separation, we show that the sparse time frequency decomposition is unique up to an error that is determined by the scale separation property of the signal. We further show that the unique decomposition can be obtained approximately by the sparse time frequency decomposition using nonlinear matching pursuit.

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.

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough numerical treatment. In this paper, we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity. Therein, local corrector problems are constructed in line with the static equations, whereas we propose to consider the full system. This allows to benefit from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure. We prove the optimal first-order convergence of this method and verify the result by numerical experiments.