Multiscale Modeling & Simulation 

About: Multiscale Modeling & Simulation is an academic journal published by Society for Industrial and Applied Mathematics. The journal publishes majorly in the area(s): Homogenization (chemistry) & Finite element method. It has an ISSN identifier of 1540-3459. Over the lifetime, 1109 publications have been published receiving 48395 citations. The journal is also known as: Multiscale modeling and simulation & MMS.

A Review of Image Denoising Algorithms, with a New One

Abstract: The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics In spite of the sophistication of the recently proposed methods, m

Signal recovery by proximal forward-backward splitting ∗

Abstract: We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems. Recent results on monotone operator splitting methods are applied to establish the convergence of a forward-backward algorithm to solve the generic problem. In turn, we recover, extend, and provide a simplified analysis for a variety of existing iterative methods. Applications to geometry/texture image decomposition schemes are also discussed. A novelty of our framework is to use extensively the notion of a proximity operator, which was introduced by Moreau in the 1960s.

Fast Discrete Curvelet Transforms

Abstract: This paper describes two digital implementations of a new mathematical transform, namely, the second generation curvelet transform in two and three dimensions. The first digital transformation is based on unequally spaced fast Fourier transforms, while the second is based on the wrapping of specially selected Fourier samples. The two implementations essentially differ by the choice of spatial grid used to translate curvelets at each scale and angle. Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. And both implementations are fast in the sense that they run in O(n^2 log n) flops for n by n Cartesian arrays; in addition, they are also invertible, with rapid inversion algorithms of about the same complexity. Our digital transformations improve upon earlier implementations—based upon the first generation of curvelets—in the sense that they are conceptually simpler, faster, and far less redundant. The software CurveLab, which implements both transforms presented in this paper, is available at http://www.curvelet.org.

An Iterative Regularization Method for Total Variation-Based Image Restoration

Abstract: We introduce a new iterative regularization procedure for inverse problems based on the use of Bregman distances, with particular focus on problems arising in image processing. We are motivated by the problem of restoring noisy and blurry images via variational methods by using total variation regularization. We obtain rigorous convergence results and effective stopping criteria for the general procedure. The numerical results for denoising appear to give significant improvement over standard models, and preliminary results for deblurring/denoising are very encouraging.

Nonlocal Operators with Applications to Image Processing

Abstract: We propose the use of nonlocal operators to define new types of flows and functionals for image processing and elsewhere. A main advantage over classical PDE-based algorithms is the ability to handle better textures and repetitive structures. This topic can be viewed as an extension of spectral graph theory and the diffusion geometry framework to functional analysis and PDE-like evolutions. Some possible applications and numerical examples are given, as is a general framework for approximating Hamilton–Jacobi equations on arbitrary grids in high demensions, e.g., for control theory.