Related papers: Deconvolution Using Projections Onto The Epigraph …

A new signal processing framework based on making orthogonal Projections onto the Epigraph Set of a Convex cost function (PESC) is developed. In this way it is possible to solve convex optimization problems using the well-known Projections…

Two new optimization techniques based on projections onto convex space (POCS) framework for solving convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost…

Two new optimization techniques based on projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets…

This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

Removing speckle noise from SAR images is still an open issue. It is well know that the interpretation of SAR images is very challenging and despeckling algorithms are necessary to improve the ability of extracting information. An urban…

Projections onto sets are used in a wide variety of methods in optimization theory but not every method that uses projections really belongs to the class of projection methods as we mean it here. Here projection methods are iterative…

We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating…

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…

This paper is concerned with a constrained optimization problem over a directed graph (digraph) of nodes, in which the cost function is a sum of local objectives, and each node only knows its local objective and constraints. To…

Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that are currently used to solve this reconstruction…

The projection onto the epigraph or a level set of a closed proper convex function can be achieved by finding a root of a scalar equation that involves the proximal operator as a function of the proximal parameter. This paper develops the…

Visualizing graphs using virtual physical models is probably the most heavily used technique for drawing graphs in practice. There are many algorithms that are efficient and produce high-quality layouts. If one requires that the layout also…

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…

This article demonstrates how an understanding of the geometry of a family of cost functions can be used to develop efficient numerical algorithms for real-time optimisation. Crucially, it is not the geometry of the individual functions…

This paper is devoted to the general problem of projection onto a polyhedral convex cone generated by a finite set of generators.This problem is reformulated into projection onto the polytope obtained by simple truncation of the original…

This paper studies a variant of the minimum-cost flow problem in a graph with convex cost function where the demands at the vertices are functions depending on a one-dimensional parameter $\lambda$. We devise two algorithmic approaches for…

Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…

In this paper we provide an efficient computation of the projection onto the cone generated by the epigraph of the perspective of any convex lower semicontinuous function. Our formula requires solving only two scalar equations involving the…

Convex optimizers have known many applications as differentiable layers within deep neural architectures. One application of these convex layers is to project points into a convex set. However, both forward and backward passes of these…