Maximum-Likelihood Deconvolution - Mendel, Jerry M.

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Biographie:
Jerry M. Mendel received the Ph.D. degree in Electrical Engineering from the Polytechnic Institute of Brooklyn, Brooklyn, NY. Currently, he is Emeritus Professor of Electrical Engineering at the University of Southern California in Los Angeles, where he worked for 44 years. He has published close to 600 technical papers and is author and/or co-author of 12 books, including Uncertain Rule-based Fuzzy Logic Systems: Introduction and New Directions (Prentice-Hall, 2001), Perceptual Computing: Aiding People in Making Subjective Judgments (Wiley & IEEE Press, 2010), Introduction to Type-2 Fuzzy Logic Control: Theory and Application (Wiley & IEEE Press, 2014) and Uncertain Rule-based Fuzzy Systems: Introduction and New Directions, 2^nd ed. (Springer, 2017). He is a Life Fellow of the IEEE, a Distinguished Member of the IEEE Control Systems Society, and a Fellow of the International Fuzzy Systems Association and the Asia-Pacific AI Association. He was President of the IEEE Control Systems Society in 1986, a member of the Administrative Committee of the IEEE Computational Intelligence Society for nine years, and Chairman of its Fuzzy Systems Technical Committee and the Computing With Words Task Force of that TC. Among his awards are the 1983 Best Transactions Paper Award of the IEEE Geoscience and Remote Sensing Society, the 1992 Signal Processing Society Paper Award, the 2002 and 2014 Transactions on Fuzzy Systems Outstanding Paper Awards, a 1984 IEEE Centennial Medal, an IEEE Third Millenium Medal, a Fuzzy Systems Pioneer Award (2008) from the IEEE Computational Intelligence Society for fundamental theoretical contributions and seminal results in fuzzy systems, and the 2021 IEEE Lotfi A. Zadeh Pioneer Award for developing and promoting type-2 fuzzy logic. As of March 27, 2023, his publications have been cited (Google Scholar) more than 63,000 times, with an h-index of 100 and an i10-index of 320....

Sommaire:
1 - Introduction.- 1.1 Introduction.- 1.2 Our Approach.- 1.3 Likelihood Versus Probability.- 1.4 Maximum-Likelihood Method.- 1.5 Comments.- 2 - Convolutional Model.- 2.1 Introduction.- 2.2 The Seismic Convolutional Model.- 2.3 Input.- 2.4 Channel Model IR (Seismic Wavelet).- 2.5 Measurement Noise.- 2.6 Other Effects.- 2.7 Mathematical Model.- 2.8 Summary.- 3 - Likelihood.- 3.1 Introduction.- 3.2 Loglikelihood.- 3.3 Likelihood Function.- 3.4 Using Given Information.- 3.5 Message for the Reader.- 3.6 Mathematical Likelihood Functions.- 3.7 Mathematical Loglikelihood Functions.- 3.8 Summary.- 4 - Maximizing Likelihood.- 4.1 Introduction.- 4.2 A Rationale.- 4.3 Block Component Search Algorithms.- 4.4 Mathematical Fact.- 4.5 Separation Principle.- 4.6 Update Random Parameters.- 4.7 Binary Detection.- 4.8 Update Wavelet Parameters.- 4.9 Update Statistical Parameters.- 4.10 Message for the Reader.- 4.11 Summary.- 5 - Properties and Performance.- 5.1 Introduction.- 5.2 Minimum-Variance Deconvolution.- 5.3 Detectors.- 5.4 A Modified Likelihood Function.- 5.5 An Objective Function.- 5.6 Marquardt-Levenberg Algorithm.- 5.7 Convergence.- 5.8 Entropy Interpretation.- 5.9 Summary.- 6 - Examples.- 6.1 Introduction.- 6.2 Some Real Data Examples.- 6.3 Minimum-Variance Deconvolution.- 6.4 Detection.- 6.5 Block Component Method.- 6.6 Backscatter.- 6.7 Noncausal Channel Models.- 6.8 Summary.- 7 - Mathematical Details for Chapter 4.- 7.1 Introduction.- 7.2 Mathematical Fact.- 7.3 Separation Principle.- 7.4 Minimum-Variance Deconvolution.- 7.5 Threshold Detector.- 7.6 Single Most-Likely Replacement Detector.- 7.7 Single Spike Shift Detector.- 7.8 SSS-SMLR Detector.- 7.9 Marquardt-Levenberg Algorithm.- 7.10 Calculating Gradients.- 7.11 Calculating Second Derivatives.- 7.12 Why vr Cannot be Estimated: Maximization of L or M is an Ill-Posed Problem.- 7.13 An Algorithm for ?.- 8 - Mathematical Details for Chapter 5.- 8.1 Introduction.- 8.2 MVD Filter Properties.- 8.3 Threshold Detector.- 8.4 Modified Likelihood Function.- 8.5 Separation Principle for P and Derivation of N from P.- 8.6 Why vr Cannot be Estimated: Maximization of P or N is not an Ill-Posed Problem.- 8.7 SMLR1 Detector Based on N.- 8.8 Quadratic Convergence of the Newton-Raphson Algorithm.- 8.9 Wavelet Identifiability.- 8.10 Convergence of Adaptive SMLR Detector.- 9 - Computational Considerations.- 9.1 Introduction.- 9.2 Recursive Processing.- 9.3 Summary.- References.