Parallel Operator Splitting Algorithms with Application to Imaging Inverse Problems

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.

Autorentext

Chuan He is an associate professor in the High-Tech Institute of Xi'an. He has been engaged in teaching and research in image processing and navigation guidance for a long time and has a deep research in the field of image restoration. He presided over 10 scientific research projects such as National Natural Science Fund, published 20 papers, won the Excellent Doctoral Dissertation Award of Shaanxi Province, and won 3 provincial and ministerial scientific research awards. He was selected into the Special Support Program for the top young talents of Shaanxi Province and technology stars of Shaanxi Province. Besides, he is a reviewer of more than ten international journals including IEEE TIP/TNNLS/TMM. Chuanghua Hu received the B. Eng. and M. Eng. degrees from the High-Tech Institute of Xi'an, Xi'an, China, in 1987 and 1990, respectively, and the Ph.D. degree from the Northwestern Polytechnic University, Xi'an, China, in 1996. He is currently a Cheung Kong Professor with the High-Tech Institute of Xi'an, Shaanxi, China. He was a Visiting Scholar with the University of Duisburg, Duisburg, Germany (September 2008-December 2008). He has authored or coauthored two books and about 100 articles. His research interests include signal processing, fault diagnosis and prediction, life prognosis, and fault tolerant control.