High-dimensional data analysis has motivated a spectrum of regularization methods for variable selection and sparse modeling, with two popular methods being convex and concave ones. A long debate has taken place on whether one class dominates the other, an important question both in theory and to practitioners. In this article, we characterize the asymptotic equivalence of regularization method...

The deconvolution in image processing is an inverse illposed problem which necessitates a trade-off between delity to data and smoothness of a solution adjusted by a regularization parameter. In this paper we propose two techniques for selection of a varying regularization parameter minimizing the mean squared error for every pixel of the image. The rst algorithm uses the estimate of the square...

We propose an information complexity-based regularization parameter selection method for solution of ill-conditioned inverse problems. The regularization parameter is selected to be the minimizer of the Kullback-Leibler (KL) distance between the unknown data-generating distribution and the fitted distribution. The KL distance is approximated by an information complexity (ICOMP) criterion develo...

Quadratic programs arise in robotics, communications, smart grids, and many other applications. As these problems grow size, finding solutions becomes more computationally demanding, new algorithms are needed to efficiently solve them at massive scales. Targeting large-scale problems, we develop a multiagent quadratic programming framework which each agent updates only small number of the total...

Convex 1-D first-order total variation (TV) denoising is an effective method for eliminating signal noise, which can be defined as convex optimization consisting of a quadratic data fidelity term and a non-convex regularization term. It not only ensures strict convex for optimization problems, but also improves the sparseness of the total variation term by introducing the non-convex penalty fun...

In image processing applications, image intensity is often measured via the counting of incident photons emitted by the object of interest. In such cases, image data-noise is accurately modeled by a Poisson distribution. This motivates the use of Poisson maximum likelihood estimation for image reconstruction. However, when the underlying model equation is ill-posed, regularization is needed. Re...