Geometry of the Phase Retrieval Problem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry of the Phase Retrieval Problem write by Alexander H. Barnett. This book was released on 2022-05-05. Geometry of the Phase Retrieval Problem available in PDF, EPUB and Kindle. This book provides a theoretical foundation and conceptual framework for the problem of recovering the phase of the Fourier transform.
Nanoscale Photonic Imaging
Nanoscale Photonic Imaging - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nanoscale Photonic Imaging write by Tim Salditt. This book was released on 2020-06-09. Nanoscale Photonic Imaging available in PDF, EPUB and Kindle. This open access book, edited and authored by a team of world-leading researchers, provides a broad overview of advanced photonic methods for nanoscale visualization, as well as describing a range of fascinating in-depth studies. Introductory chapters cover the most relevant physics and basic methods that young researchers need to master in order to work effectively in the field of nanoscale photonic imaging, from physical first principles, to instrumentation, to mathematical foundations of imaging and data analysis. Subsequent chapters demonstrate how these cutting edge methods are applied to a variety of systems, including complex fluids and biomolecular systems, for visualizing their structure and dynamics, in space and on timescales extending over many orders of magnitude down to the femtosecond range. Progress in nanoscale photonic imaging in Göttingen has been the sum total of more than a decade of work by a wide range of scientists and mathematicians across disciplines, working together in a vibrant collaboration of a kind rarely matched. This volume presents the highlights of their research achievements and serves as a record of the unique and remarkable constellation of contributors, as well as looking ahead at the future prospects in this field. It will serve not only as a useful reference for experienced researchers but also as a valuable point of entry for newcomers.
Phase retrieval problems in x-ray physics
Phase retrieval problems in x-ray physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Phase retrieval problems in x-ray physics write by Carolin Homann. This book was released on 2015. Phase retrieval problems in x-ray physics available in PDF, EPUB and Kindle. In phase retrieval problems that occur in imaging by coherent x-ray diffraction, one tries to reconstruct information about a sample of interest from possibly noisy intensity measurements of the wave fi eld traversing the sample. The mathematical formulation of these problems bases on some assumptions. Usually one of them is that the x-ray wave fi eld is generated by a point source. In order to address this very idealized assumption, it is common to perform a data preprocessing step, the so-called empty beam correction. Within this work, we study the validity of this approach by presenting a quantitative error estimate. Moreover, in order to solve these phase retrieval problems, we want to incorporate a priori knowledge about the structure of the noise and the solution into the reconstruction process. For this reason, the application of a problem adapted iteratively regularized Newton-type method becomes particularly attractive. This method includes the solution of a convex minimization problem in each iteration step. We present a method for solving general optimization problems of this form. Our method is a generalization of a commonly used algorithm which makes it efficiently applicable to a wide class of problems. We also proof convergence results and show the performance of our method by numerical examples.
Image Recovery: Theory and Application
Image Recovery: Theory and Application - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Image Recovery: Theory and Application write by Henry Stark. This book was released on 2013-04-25. Image Recovery: Theory and Application available in PDF, EPUB and Kindle. Image Recovery: Theory and Application focuses on signal recovery and synthesis problems. This book discusses the concepts of image recovery, including regularization, the projection theorem, and the pseudoinverse operator. Comprised of 13 chapters, this volume begins with a review of the basic properties of linear vector spaces and associated operators, followed by a discussion on the Gerchberg-Papoulis algorithm. It then explores image restoration and the basic mathematical theory in image restoration problems. The reader is also introduced to the problem of obtaining artifact-free computed tomographic reconstruction. Other chapters consider the importance of Bayesian approach in the context of medical imaging. In addition, the book discusses the linear programming method, which is particularly important for images with large number of pixels with zero value. Such images are usually found in medical imaging, microscopy, electron microscopy, and astronomy. This book can be a valuable resource to materials scientists, engineers, computed tomography technologists, and astronomers.
Sparse Solutions of Underdetermined Linear Systems and Their Applications
Sparse Solutions of Underdetermined Linear Systems and Their Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sparse Solutions of Underdetermined Linear Systems and Their Applications write by Ming-Jun Lai . This book was released on 2021-06-25. Sparse Solutions of Underdetermined Linear Systems and Their Applications available in PDF, EPUB and Kindle. This textbook presents a special solution to underdetermined linear systems where the number of nonzero entries in the solution is very small compared to the total number of entries. This is called a sparse solution. Since underdetermined linear systems can be very different, the authors explain how to compute a sparse solution using many approaches. Sparse Solutions of Underdetermined Linear Systems and Their Applications contains 64 algorithms for finding sparse solutions of underdetermined linear systems and their applications for matrix completion, graph clustering, and phase retrieval and provides a detailed explanation of these algorithms including derivations and convergence analysis. Exercises for each chapter help readers understand the material. This textbook is appropriate for graduate students in math and applied math, computer science, statistics, data science, and engineering. Advisors and postdoctoral scholars will also find the book interesting and useful.
