With information and scale as central themes, this comprehensive survey explains how to
handle real problems in astronomical data analysis using a modern arsenal of powerful …

This article reviews bandlet approaches to geometric image representations. Orthogonal
bandlets using an adaptive segmentation and a local geometric flow well suited to capture …

Suppose x is an unknown vector in Ropf m (a digital image or signal); we plan to measure n
general linear functionals of x and then reconstruct. If x is known to be compressible by …

Suppose we are given a vector< emphasis>< formula formulatype=" inline">< tex>
f</tex></formula></emphasis> in a class< emphasis>< formula formulatype=" inline">< tex> …

A full-rank matrix \bfA∈R^n*m with n<m generates an underdetermined system of linear
equations \bfAx=\bfb having infinitely many solutions. Suppose we seek the sparsest …

This is a survey of nonlinear approximation, especially that part of the subject which is
important in numerical computation. Nonlinear approximation means that the approximants …

This book presents the state of the art in sparse and multiscale image and signal processing,
covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and …

Image inpainting is a special image restoration problem for which image prior models play a
crucial role. Euler's elastica was first introduced to computer vision by Mumford [Algebraic …

This paper introduces a new class of bases, called bandelet bases, which decompose the
image along multiscale vectors that are elongated in the direction of a geometric flow. This …

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2003. This book contains
a detailed mathematical analysis of the variational approach to image restoration based on …