Parallel image restoration

Cataloged from PDF version of article.In this thesis, we are concerned with the image restoration problem which has been formulated in the literature as a system of linear inequalities. With this formulation, the resulting constraint matrix is an unstructured sparse-matrix and even with small size images we end up with huge matrices. So, to solve the restoration problem, we have used the surrogate constraint methods, that can work efficiently for large size problems and are amenable for parallel implementations. Among the surrogate constraint methods, the basic method considers all of the violated constraints in the system and performs a single block projection in each step. On the other hand, parallel method considers a subset of the constraints, and makes simultaneous block projections. Using several partitioning strategies and adopting different communication models we have realized several parallel implementations of the two methods. We have used the hypergraph partitioning based decomposition methods in order to minimize the communication costs while ensuring load balance among the processors. The implementations are evaluated based on the per iteration performance and on the overall performance. Besides, the effects of different partitioning strategies on the speed of convergence are investigated. The experimental results reveal that the proposed parallelization schemes have practical usage in the restoration problem and in many other real-world applications which can be modeled as a system of linear inequalities.Malas, TahirM.S

Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio