Title Local approximation techniques in signal and image processing / Vladimir Katkovnik, Karen Egiazarian, and Jaakko Astola

Published Bellingham, Wash. : SPIE, 2006

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Description 1 online resource (xvii, 553 pages) : illustrations Series SPIE Press monograph ; PM157 SPIE monograph ; PM157 Contents 1. Introduction -- 1.1. Linear local approximation -- 1.2. Anisotropy -- 1.3. Nonlinear local approximation -- 1.4. Multiresolution analysis -- 1.5. Imaging applications -- 1.6. Overview of the book 2. Discrete LPA -- 2.1. Introduction -- 2.2. Basis of LPA -- 2.3. Kernel LPA estimates -- 2.4. Nonparametric regression -- 2.5. Nonparametric interpolation 3. Shift-invariant LPA kernels -- 3.1. Regular grid kernels -- 3.2. Vanishing moments -- 3.3. Frequency domain -- 3.4. Numerical shift-invariant kernels -- 3.5. Numerical differentiation 4. Integral LPA -- 4.1. Integral kernel estimators -- 4.2. Analytical kernels -- 4.3. Generalized singular functions -- 4.4. Potential derivative estimates 5. Discrete LPA accuracy -- 5.1. Bias and variance of estimates -- 5.2. Ideal scale -- 5.3. Accuracy of potential differentiators 6. Adaptive-scale selection -- 6.1. ICI rule -- 6.2. Multiple-window estimation -- 6.3. Denoising experiments 7. Anisotropic LPA -- 7.1. Directional signal processing -- 7.2. Directional LPA -- 7.3. Numerical directional kernels 8. Anisotropic LPA-ICI algorithms -- 8.1. Accuracy analysis -- 8.2. Adaptive-scale algorithms -- 8.3. Directional image denoising -- 8.4. Directional differentiation -- 8.5. Shading from depth -- 8.6. Optical flow estimation 9. Image reconstruction -- 9.1. Image deblurring -- 9.2. LPA-ICI deblurring algorithms -- 9.3. Motion deblurring -- 9.4. Super-resolution imaging -- 9.5. Inverse halftoning -- 9.6. 3D inverse 10. Nonlinear methods -- 10.1. Why nonlinear methods? -- 10.2. Robust M-estimation -- 10.3. LPA-ICI robust M-estimates -- 10.4. Nonlinear transform methods 11. Likelihood and quasi-likelihood -- 11.1. Local maximum likelihood -- 11.2. Binary and counting observations -- 11.3. Local quasi-likelihood -- 11.4. Quasi-likelihood LPA-ICI algorithms 12. Photon imaging -- 12.1. Direct Poisson observations -- 12.2. Indirect Poisson observations -- 12.3. Local ML Poisson inverse -- 12.4. Computerized tomography 13. Multiresolution analysis -- 13.1. MR analysis: basic concepts -- 13.2. Nonparametric LPA spectrum -- 13.3. Thresholding -- 13.4. Parallels with wavelets 14. Appendix -- 14.1. Analytical regular grid kernels -- 14.2. LPA accuracy -- 14.3. ICI rule -- 14.4. Cross validation -- 14.5. Directional LPA accuracy -- 14.6. Random processes -- 14.7. 3D inverse -- 14.8. Nonlinear methods -- References -- Index Summary This book deals with a wide class of novel and efficient adaptive signal processing techniques developed to restore signals from noisy and degraded observations. These signals include those acquired from still or video cameras, electron microscopes, radar, x rays, or ultrasound devices, and are used for various purposes, including entertainment, medical, business, industrial, military, civil, security, and scientific applications. In many cases useful information and high quality must be extracted from the imaging. However, often raw signals are not directly suitable for this purpose and must be processed in some way. Such processing is called signal reconstruction. This book is devoted to a recent and original approach to signal reconstruction based on combining two independent ideas: local polynomial approximation and the intersection of confidence interval rule Bibliography Includes bibliographical references (pages 535-546) and index Notes Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL Subject Approximation theory. Image processing -- Mathematics Signal processing -- Mathematics TECHNOLOGY & ENGINEERING -- Mechanical. Approximation theory Image processing -- Mathematics Signal processing -- Mathematics Approximationstheorie Bildverarbeitung Mathematik Signalverarbeitung Form Electronic book Author Astola, Jaakko. Egiazarian, K. (Karen), 1959- Society of Photo-Optical Instrumentation Engineers ISBN 9780819478337 0819478334

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