36 citations · 47 across the 12 of their papers we have counts for
12 papers
The Proximity Operator of the Log-Sum Penalty
Ashley Prater-Bennette, Lixin Shen, Erin E. Tripp
The log-sum penalty is often adopted as a replacement for the pseudo-norm in compressive sensing and low-rank optimization. The hard-thresholding operator, i.e., the proxi…
Regularization with Multilevel Non-stationary Tight Framelets for Image Restoration
Yan-ran Li, Raymond H. F. Chan, Lixin Shen +1
Variational regularization models are one of the popular and efficient approaches for image restoration. The regularization functional in the model carries prior knowledge about th…
Multiplicative Noise Removal: Nonlocal Low-Rank Model and Its Proximal Alternating Reweighted Minimization Algorithm
Xiaoxia Liu, Jian Lu, Lixin Shen +2
The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices f…
On Distributed Online Convex Optimization with Sublinear Dynamic Regret and Fit
Pranay Sharma, Prashant Khanduri, Lixin Shen +2
In this work, we consider a distributed online convex optimization problem, with time-varying (potentially adversarial) constraints. A set of nodes, jointly aim to minimize a globa…
Algorithmic Versatility of SPF-regularization Methods
Lixin Shen, Bruce W. Suter, Erin E. Tripp
Sparsity promoting functions (SPFs) are commonly used in optimization problems to find solutions which are assumed or desired to be sparse in some basis. For example, the l1-regula…
Structured Sparsity Promoting Functions
Lixin Shen, Bruce W. Suter, Erin E. Tripp
Motivated by the minimax concave penalty based variable selection in high-dimensional linear regression, we introduce a simple scheme to construct structured semiconvex sparsity pr…
Sparse tensor recovery via N-mode FISTA with support augmentation
Ashley Prater-Bennette, Lixin Shen
A common approach for performing sparse tensor recovery is to use an N-mode FISTA method. However, this approach may fail in some cases by missing some values in the true support o…
A Super-Resolution Framework for Tensor Decomposition
Qiuwei Li, Ashley Prater, Lixin Shen +1
This work considers a super-resolution framework for overcomplete tensor decomposition. Specifically, we view tensor decomposition as a super-resolution problem of recovering a sum…
Finding Dantzig selectors with a proximity operator based fixed-point algorithm
Ashley Prater, Lixin Shen, Bruce W. Suter
In this paper, we study a simple iterative method for finding the Dantzig selector, which was designed for linear regression problems. The method consists of two main stages. The f…
Separation of undersampled composite signals using the Dantzig selector with overcomplete dictionaries
Ashley Prater, Lixin Shen
In many applications one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one a…
Blind One-Bit Compressive Sampling
Lixin Shen, Bruce W. Suter
The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model tar…
Efficient First Order Methods for Linear Composite Regularizers
Andreas Argyriou, Charles A. Micchelli, Massimiliano Pontil +2
A wide class of regularization problems in machine learning and statistics employ a regularization term which is obtained by composing a simple convex function ωwith a linear trans…