Inverse Methods Applied to DSP

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.

Jean-François Giovannelli is Professor at the University of Bordeaux in France and carried out research at the IMS laboratory into signal and image processing. His contributions concern inverse problems, deterministic and Bayesian regularization and in particular myopic and unsupervised aspects.

Jérôme Idier is CNRS Director of Research at IRCCyN in Nantes, France. He is a member of the French national committee for scientific research. His research work concerns inference and optimization for the solution of inverse problems in signal and image processing.