Parallel Operator Splitting Algorithms with Application to Imaging Inverse Problems [electronic resource] /

Introduction -- Mathematical Fundamentals -- Ill-poseness of imaging inverse problems and regularization for detail preservation -- Fast parameter estimation in TV-based image restoration -- Parallel alternating derection method of multipliers with application to image restoration -- Parallel primal-dual method with application to image restoration.

Image denoising, image deblurring, image inpainting, super-resolution, and compressed sensing reconstruction have important application value in engineering practice, and they are also the hot frontiers in the field of image processing. This book focuses on the numerical analysis of ill condition of imaging inverse problems and the methods of solving imaging inverse problems based on operator splitting. Both algorithmic theory and numerical experiments have been addressed. The book is divided into six chapters, including preparatory knowledge, ill-condition numerical analysis and regularization method of imaging inverse problems, adaptive regularization parameter estimation, and parallel solution methods of imaging inverse problem based on operator splitting. Although the research methods in this book take image denoising, deblurring, inpainting, and compressed sensing reconstruction as examples, they can also be extended to image processing problems such as image segmentation, hyperspectral decomposition, and image compression. This book can benefit teachers and graduate students in colleges and universities, or be used as a reference for self-study or further study of image processing technology engineers. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.