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Maximum-Likelihood Deconvolution

A Journey into Model-Based Signal Processing

  • Jerry M. Mendel

Part of the Signal Processing and Digital Filtering book series (SIGNAL PROCESS)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Jerry M. Mendel
    Pages 1-6
  3. Jerry M. Mendel
    Pages 7-23
  4. Jerry M. Mendel
    Pages 25-30
  5. Jerry M. Mendel
    Pages 31-59
  6. Jerry M. Mendel
    Pages 61-76
  7. Jerry M. Mendel
    Pages 77-125
  8. Jerry M. Mendel
    Pages 127-171
  9. Jerry M. Mendel
    Pages 173-185
  10. Jerry M. Mendel
    Pages 187-208
  11. Back Matter
    Pages 209-227

About this book

Introduction

Convolution is the most important operation that describes the behavior of a linear time-invariant dynamical system. Deconvolution is the unraveling of convolution. It is the inverse problem of generating the system's input from knowledge about the system's output and dynamics. Deconvolution requires a careful balancing of bandwidth and signal-to-noise ratio effects. Maximum-likelihood deconvolution (MLD) is a design procedure that handles both effects. It draws upon ideas from Maximum Likelihood, when unknown parameters are random. It leads to linear and nonlinear signal processors that provide high-resolution estimates of a system's input. All aspects of MLD are described, from first principles in this book. The purpose of this volume is to explain MLD as simply as possible. To do this, the entire theory of MLD is presented in terms of a convolutional signal generating model and some relatively simple ideas from optimization theory. Earlier approaches to MLD, which are couched in the language of state-variable models and estimation theory, are unnecessary to understand the essence of MLD. MLD is a model-based signal processing procedure, because it is based on a signal model, namely the convolutional model. The book focuses on three aspects of MLD: (1) specification of a probability model for the system's measured output; (2) determination of an appropriate likelihood function; and (3) maximization of that likelihood function. Many practical algorithms are obtained. Computational aspects of MLD are described in great detail. Extensive simulations are provided, including real data applications.

Keywords

Signal entropy filter filters information model simulation

Authors and affiliations

  • Jerry M. Mendel
    • 1
  1. 1.Department of Electrical Engineering-SystemsUniversity of Southern CaliforniaLos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-3370-1
  • Copyright Information Springer-Verlag New York 1990
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7985-3
  • Online ISBN 978-1-4612-3370-1
  • Series Print ISSN 1431-7893
  • Buy this book on publisher's site
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