A Douglas-Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery
نویسنده
چکیده
Under consideration is the large body of signal recovery problems that can be formulated as the problem of minimizing the sum of two (not necessarily smooth) lower semicontinuous convex functions in a real Hilbert space. This generic problem is analyzed and a decomposition method is proposed to solve it. The convergence of the method, which is based on the Douglas-Rachford algorithm for monotone operator-splitting, is obtained under general conditions. Applications to non-Gaussian image denoising in a tight frame are also demonstrated.
منابع مشابه
Lecture 20 : Splitting Algorithms
In this lecture, we discuss splitting algorithms for convex minimization problems with objective given by the sum of two nonsmooth functions. We start with the fixed point property of such problems and derive a general scheme of splitting algorithm based on fixed point iteration. This covers Douglas-Rachford splitting and Peaceman-Rachford splitting algorithms. We also discuss the convergence r...
متن کاملA Primal-Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms
We propose a new first-order splitting algorithm for solving jointly the primal and dual formulations of large-scale convex minimization problems involving the sum of a smooth function with Lipschitzian gradient, a nonsmooth proximable function, and linear composite functions. This is a full splitting approach, in the sense that the gradient and the linear operators involved are applied explici...
متن کاملA Note on the Forward-Douglas–Rachford Splitting for Monotone Inclusion and Convex Optimization
We shed light on the structure of the “three-operator” version of the forward-Douglas– Rachford splitting algorithm for nding a zero of a sum of maximally monotone operators A+B+C, where B is cocoercive, involving only the computation of B and of the resolvent ofA and of C, separately. We show that it is a straightforward extension of a xed-point algorithm proposed by us as a generalization o...
متن کاملTheory and Applications of Convex and Non-convex Feasibility Problems
Let X be a Hilbert space and let Cn, n = 1, . . . ,N be convex closed subsets of X . The convex feasibility problem is to find some point x ∈ N ⋂ n=1 Cn, when this intersection is non-empty. In this talk we discuss projection algorithms for finding such a feasibility point. These algorithms have wide ranging applications including: solutions to convex inequalities, minimization of convex nonsmo...
متن کاملOn the Range of the Douglas-Rachford Operator
The problem of finding a minimizer of the sum of two convex functions — or, more generally, that of finding a zero of the sum of two maximally monotone operators — is of central importance in variational analysis. Perhaps the most popular method of solving this problem is the Douglas–Rachford splitting method. Surprisingly, little is known about the range of the Douglas–Rachford operator. In th...
متن کامل