This paper introduces a novel algorithm to approximate the matrix with minimum nuclear
norm among all matrices obeying a set of convex constraints. This problem may be …

Split Bregman methods introduced in [T. Goldstein and S. Osher, SIAM J. Imaging Sci., 2
(2009), pp. 323–343] have been demonstrated to be efficient tools for solving total variation …

The variational techniques (eg the total variation based method) are well established and
effective for image restoration, as well as many other applications, while the wavelet frame …

As a rapidly growing, multidisciplinary field of mathematics, wavelet theory provides the
major mathematical multiscale representation for analyzing functions/data and has …

Finding a solution of a linear equation $ Au= f $ with various minimization properties arises
from many applications. One such application is compressed sensing, where an efficient …

Real images usually have sparse approximations under some tight frame systems derived
from framelets, an oversampled discrete (window) cosine, or a Fourier transform. In this …

One of the key steps in compressed sensing is to solve the basis pursuit problem $\min _
{u\in\mathbb {R}^ n}\{\| u\| _1: Au= f\} $. Bregman iteration was very successfully used to …

This collection of lecture notes is based on a series of lectures presented by the authors at
the Institute for Advanced Studies/Park City Mathematics 2010 Summer Program on “The …

In this paper, we introduce a new (constructive) characterization of tight wavelet frames on
non-flat domains in both continuum setting, ie on manifolds, and discrete setting, ie on …

One of the major driven forces in the area of applied and computational harmonic analysis
over the last decade or longer is the development of redundant systems that have sparse …