We propose a novel method for constructing wavelet transforms of functions defined on the
vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling …

Fully updated throughout, with several new chapters, this second edition of Introduction to
Inverse Problems in Imaging guides advanced undergraduate and graduate students in …

Imaging is an interdisciplinary research area with profound applications in many areas of
science, engineering, technology, and medicine. The most primitive form of imaging is visual …

This paper explores various aspects of the image decomposition problem using modern
variational techniques. We aim at splitting an original image f into two components u and ρ …

Pansharpening aims to fuse a multispectral (MS) image with low spatial resolution and a
panchromatic (PAN) image with a high-spatial resolution to produce an image with both high …

In this paper, we study alternating direction methods for solving constrained total-variation
image restoration and reconstruction problems. Alternating direction methods can be …

Regularization of ill-posed linear inverse problems via ℓ 1 penalization has been proposed
for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer …

This article provides a variational formulation for hard and firm thresholding. A related
functional can be used to regularize inverse problems by sparsity constraints. We show that …

The notion of soft thresholding plays a central role in problems from various areas of applied
mathematics, in which the ideal solution is known to possess a sparse decomposition in …

Vector-valued data appearing in concrete applications often possess sparse expansions
with respect to a preassigned frame for each vector component individually. Additionally …