Description
Book SynopsisThis book is devoted to the study of variational methods in imaging. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.
Trade ReviewFrom the reviews:
"Imaging is a wide area of applied mathematics which covers inverse problems, data filtering … medical diagnosis, etc. … The book is structured in a logical manner, starting with motivating examples and building on them. … One of the strengths of this book is its real-life applications and analytical and numerical results presented at each step, keeping the content real … . This is … a book for the seasoned researchers or graduate students who look to deepen their understanding of the subject." (Bogdan G. Nita, Mathematical Reviews, Issue 2009 j)
“The book is mainly devoted to variational methods in imaging. It is divided into three parts. … The book is interesting in particular for its rigorous presentation of many proved mathematical results, and is … important for the image processing community.” (Alessandro Duci, Zentralblatt MATH, Vol. 1177, 2010)
Table of ContentsFundamentals of Imaging.- Case Examples of Imaging.- Image and Noise Models.- Regularization.- Variational Regularization Methods for the Solution of Inverse Problems.- Convex Regularization Methods for Denoising.- Variational Calculus for Non-convex Regularization.- Semi-group Theory and Scale Spaces.- Inverse Scale Spaces.- Mathematical Foundations.- Functional Analysis.- Weakly Differentiable Functions.- Convex Analysis and Calculus of Variations.
