K. C. Chou

Bio: K. C. Chou is an academic researcher. The author has contributed to research in topics: Smoothing & Tree (data structure). The author has an hindex of 2, co-authored 2 publications receiving 291 citations.

Multiscale recursive estimation, data fusion, and regularization

Abstract: We describe a framework for modeling stochastic phenomena at multiple scales and for their efficient estimation or reconstruction given partial and/or noisy measurements which may also be at several scales. In particular multiscale signal representations lead naturally to pyramidal or tree-like data structures in which each level in the tree corresponds to a particular scale of representation. A class of multiscale dynamic models evolving on dyadic trees is introduced. The main focus of this paper is on the description, analysis, and application of an extremely efficient optimal estimation algorithm for this class of models. This algorithm consists of a fine-to-coarse filtering sweep, followed by a coarse-to-fine smoothing step, corresponding to the dyadic tree generalization of Kalman filtering and Rauch-Tung-Striebel smoothing. The Kalman filtering sweep consists of the recursive application of three steps: a measurement update step, a fine-to-coarse prediction step, and a fusion step. We illustrate the use of our methodology for the fusion of multiresolution data and for the efficient solution of "fractal regularizations" of ill-posed signal and image processing problems encountered. >

Multiscale Statistical Signal Processing: Stochastic Processes Indexed by Trees

Abstract: Motivated by the recently-developed theory of multiscale signal models and wavelet transforms, we introduce stochastic dynamic models evolving on homogeneous trees. In particular we introduce and investigate both AR and state models on trees. Our analysis yields generalizations of Levinson and Schur recursions and of Kalman filters, Riccati equations, and Rauch-Tung-Striebel smoothing.

Multirate digital signal processing

Abstract: There has been a great deal of material in the area of discrete-time transforms that has been published in recent years. This book does an excellent job of presenting important aspects of such material in a clear manner. The book has 11 chapters and a very useful appendix. Seven of these chapters are essentially devoted to the Fourier series/transform, discrete Fourier transform, fast Fourier transform (FFT), and applications of the FFT in the area of spectral estimation. Chapters 8 through 10 deal with many other discrete-time transforms and algorithms to compute them. Of these transforms, the KarhunenLoeve, the discrete cosine, and the Walsh-Hadamard transform are perhaps the most well-known. A lucid discussion of number theoretic transforms i5 presented in Chapter 11. This reviewer feels that the authors have done a fine job of compiling the pertinent material and presenting it in a concise and clear manner. There are a number of problems at the end of each chapter, an appreciable number of which are challenging. The authors have included a comprehensive set of references at the end of the book. In brief, this book is a valuable contribution to the general areas of signal processing and communications. It can be used for a graduate level course in perhaps two ways. One would be to cover the first seven chapters in great detail. The other would be to cover the whole book by focussing on different topics in a selective manner. This book by Elliott and Rao is extremely useful to researchers/engineers who are working in the areas of signal processing and communications. It i s also an excellent reference book, and hence a valuable addition to one’s library

Multiscale PCA with application to multivariate statistical process monitoring

Abstract: Multiscale principal-component analysis (MSPCA) combines the ability of PCA to decorrelate the variables by extracting a linear relationship with that of wavelet analysis to extract deterministic features and approximately decorrelate autocorrelated measurements. MSPCA computes the PCA of wavelet coefficients at each scale and then combines the results at relevant scales. Due to its multiscale nature, MSPCA is appropriate for the modeling of data containing contributions from events whose behavior changes over time and frequency. Process monitoring by MSPCA involves combining only those scales where significant events are detected, and is equivalent to adaptively filtering the scores and residuals, and adjusting the detection limits for easiest detection of deterministic changes in the measurements. Approximate decorrelation of wavelet coefficients also makes MSPCA effective for monitoring autocorrelated measurements without matrix augmentation or time-series modeling. In addition to improving the ability to detect deterministic changes, monitoring by MSPCA also simultaneously extracts those features that represent abnormal operation. The superior performance of MSPCA for process monitoring is illustrated by several examples.

A categorization of multiscale-decomposition-based image fusion schemes with a performance study for a digital camera application

Abstract: The objective of image fusion is to combine information from multiple images of the same scene. The result of image fusion is a single image which is more suitable for human and machine perception or further image-processing tasks. In this paper, a generic image fusion framework based on multiscale decomposition is studied. This framework provides freedom to choose different multiscale decomposition methods and different fusion rules. The framework includes all of the existing multiscale-decomposition-based fusion approaches we found in the literature which did not assume a statistical model for the source images. Different image fusion approaches are investigated based on this framework. Some evaluation measures are suggested and applied to compare the performance of these fusion schemes for a digital camera application. The comparisons indicate that our framework includes some new approaches which outperform the existing approaches for the cases we consider.

Multiresolution Markov models for signal and image processing

Abstract: Reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts-in particular, making ties to topics such as wavelets and multigrid methods. A third goal is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for self-similar and 1/f processes. We also illustrate how these methods have been used in practice.