The focus of this book is on "ill-posed inverse problems". These problems cannot be solved only on the basis of observed data. The building of solutions involves the recognition of other pieces of a priori information. These solutions are then specific to the pieces of information taken into account. Clarifying and taking these pieces of information into account is necessary for grasping the domain of validity and the field of application for the solutions built. For too long, the interest in these problems has remained very limited in the signal-image community. However, the community has since recognized that these matters are more interesting and they have become the subject of much greater enthusiasm. From the application field’s point of view, a significant part of the book is devoted to conventional subjects in the field of inversion: biological and medical imaging, astronomy, non-destructive evaluation, processing of video sequences, target tracking, sensor networks and digital communications. The variety of chapters is also clear, when we examine the acquisition modalities at stake: conventional modalities, such as tomography and NMR, visible or infrared optical imaging, or more recent modalities such as atomic force imaging and polarized light imaging.

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.

In the field of image processing, many applications require real-time execution, particularly those in the domains of medicine, robotics and transmission, to name but a few. Recent technological developments have allowed for the integration of more complex algorithms with large data volume into embedded systems, in turn producing a series of new sophisticated electronic architectures at affordable prices. This book performs an in-depth survey on this topic. It is primarily written for those who are familiar with the basics of image processing and want to implement the target processing design using different electronic platforms for computing acceleration. The authors present techniques and approaches, step by step, through illustrative examples. This book is also suitable for electronics/embedded systems engineers who want to consider image processing applications as sufficient imaging algorithm details are given to facilitate their understanding.

This book aims to learn to use the basic concepts in signal processing. Each chapter is a reminder of the basic principles is presented followed by a series of corrected exercises. After resolution of these exercises, the reader can pretend to know those principles that are the basis of this theme. "We do not learn anything by word, but by example."

The aim of this book is the study of signals and deterministic systems, linear, time-invariant, finite dimensions and causal. A set of useful tools is selected for the automatic and signal processing and methods of representation of dynamic linear systems are exposed, and analysis of their behavior. Finally we discuss the estimation, identification and synthesis of control laws for the purpose of stabilization and regulation.

Color is a sensation generated both by the interaction of the visual sensors in the eyes with the natural environment and by the elaboration of visual information by higher brain functions. This book presents the mathematical framework needed to deal with several models of color processing of digital images. The book starts with a short yet exhaustive introduction to the basic phenomenological features of color vision, which are constantly used throughout the book. The discussion of computational issues starts with color constancy, which is dealt with in a rigorous and self-contained mathematical setting. Then, the original Retinex model and its numerous variants are introduced and analyzed with direct discrete equations. The remainder of the book is dedicated to the variational analysis of Retinex-like models, contextualizing their action with respect to contrast enhancement.