Salient edge selection and time-varying regularization are two crucial techniques to guarantee the success of maximum a posteriori (MAP)-based blind deconvolution. However, the existing approaches usually rely on carefully designed regularizers and handcrafted parameter tuning to obtain satisfactory estimation of the blur kernel. Many regularizers exhibit the structure-preserving smoothing capa...

The idea behind Compressive Sensing(CS) is the reconstruction of sparse signals from very few samples, by means of solving a convex optimization problem. In this paper we propose a compressive sensing framework using the Two-Step Iterative Shrinkage/ Thresholding Algorithms(TwIST) for reconstructing speech signals. Further, we compare this framework with two other convex optimization algorithms...

Image reconstruction in Electrical Resistance Tomography (ERT) is an ill-posed nonlinear inverse problem. Considering the influence of the sparse measurement data on the quality of the reconstructed image, the l1 regularized least-squares program (l1 regularized LSP), which can be cast as a second order cone programming problem, is introduced to solve the inverse problem in this paper. A normal...

In this paper, we analyze a sparse nonlinear inverse scattering problem arising in microwave imaging and numerically solved it for retrieving dielectric contrast from measured fields. In sparsity reconstruction, contrast profiles are a priori assumed to be sparse with respect to a certain base. We proposed an approach which is motivated by a Tikhonov functional incorporating a sparsity promotin...

This paper addresses signal denoising when large-amplitude coefficients form clusters (groups). The L1-norm and other separable sparsity models do not capture the tendency of coefficients to cluster (group sparsity). This work develops an algorithm, called ‘overlapping group shrinkage’ (OGS), based on the minimization of a convex cost function involving a group-sparsity promoting penalty functi...

This paper builds on a simple unified representation of shrinkage Bayes estimators based on hierarchical Normal-Gamma priors. Various popular penalized least squares estimators for shrinkage and selection in regression models can be recovered using this single hierarchical Bayes formulation. Using 129 U.S. macroeconomic quarterly variables for the period 1959 – 2010 I exhaustively evaluate the ...

Bayesian hierarchical shrinkage methods have been widely used for quantitative trait locus mapping. From the computational perspective, the application of the Markov chain Monte Carlo (MCMC) method is not optimal for high-dimensional problems such as the ones arising in epistatic analysis. Maximum a posteriori (MAP) estimation can be a faster alternative, but it usually produces only point esti...

This article derives the probability density function (pdf) of the sum of a normal random variable and a (sphered) Student’s-t distribution on three degrees of freedom. Advice is given on deriving the convolution density for higher degrees of freedom. Apart from its intrinsic interest applications of this result include Bayesian wavelet shrinkage, Bayesian posterior density derivations, calcula...

We consider recovery of low-rank matrices from noisy data by hard thresholding of singular values, in which empirical singular values below a prescribed threshold λ are set to 0. We study the asymptotic MSE (AMSE) in a framework where the matrix size is large compared to the rank of the matrix to be recovered, and the signal-to-noise ratio of the low-rank piece stays constant. The AMSE-optimal ...