Introduction. 1. Two Dimensional Systems and Mathematical Preliminaries. 2. Image Perception. 3. Image Sampling and Quantization. 4. Image Transforms. 5. Image Representation by Stochastic Models. 6. Image Enhancement. 7. Image Filtering and Restoration. 8. Image Analysis and Computer Vision. 9. Image Reconstruction From Projections. 10. Image Data Compression.

Fundamentals of digital image processing

A summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented in this tutorial. An examination of the underlying time series model assumed by each technique serves as the common basis for understanding the differences among the various spectrum analysis approaches. Techniques discussed include the classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods. A summary table in the text provides a concise overview for all methods, including key references and appropriate equations for computation of each spectral estimate.

Spectrum analysis&#8212;A modern perspective

Adaptive Signal Processing

1. Basic Concepts. 2. Nonparametric Methods. 3. Parametric Methods for Rational Spectra. 4. Parametric Methods for Line Spectra. 5. Filter Bank Methods. 6. Spatial Methods. Appendix A: Linear Algebra and Matrix Analysis Tools. Appendix B: Cramer-Rao Bound Tools. Appendix C: Model Order Selection Tools. Appendix D: Answers to Selected Exercises. Bibliography. References Grouped by Subject. Subject Index.

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Spectral analysis of signals

Introduction to linear and nonlinear programming

We present a generalization to the multichannel case of the well-known Burg maximum entropy technique for spectral estimation. The extension is obtained by first obtaining the proper generalization of the scalar reflection coefficients to the multichannel (or matrix) case.

Recursive Multichannel Maximum Entropy Spectral Estimation

We present several new algorithms, and more generally a new approach, to recursive estimation algorithms for linear dynamical systems. Earlier results in this area have been obtained by several others, especially Potter, Golub, Dyer and McReynolds, Kaminski, Schmidt, Bryson, and Bierman on what are known as square-root algorithms. Our results are more comprehensive. They also show bow constancy of parameters can be exploited to reduce the number of computations and to obtain new forms of the Chandrasekhar-type equations for computing the filter gain. Our approach is essentially based on certain simple geometric interpretations of the overall estimation problem. One of our goals is to attract attention to non-Riccati-based studies of estimation problems.

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Square-root algorithms for least-squares estimation

New inversion formulas for matrices classified in terms of their distance from Toeplitz matrices

Certain recently developed fast algorithms for recursive estimation in constant continuous-time linear systems are extended to discrete-time systems. The main feature is the replacement of the Riccati-type difference equation that is generally used for such problems by another set of difference equations that we call of Chandrasekhar-type. The total number of operations in the new algorithm is in general less than with the Riccati-equation based Kalman filter, with significant reductions being obtained in several important special cases. The algorithms are derived via a factorization of increments of the Riccati equation variable, a method that can be extended to nonsymmetric Riccati equations as well.

Some new algorithms for recursive estimation in constant, linear, discrete-time systems

During recent years, linear system theory has intensively been applied in estimation and control. At the same time, image processing has attracted increasing interest and attempts have been made to extend the techniques of systems theory to multidimensional problems, among others, by Bose, Attasi, Givone and Roesser, and Mitra. Part I of our results is centered around polynomial descriptions of systems. The notion of minimality in connection with state space requires the concept of coprimeness of 2-D polynomial matrices. For this purpose, we have extended the existing 1-D results on greatest common right divisor (GCRD) extraction, Sylvester resultants, matrix fraction descriptions (MFD) to the 2-D case. In addition we have results that appear to be unique for multidimensional problems such as existence and uniqueness of so-called "primitive factorizations" and existence of general factorizations. Part II will appear in a companion paper presenting results on a comparison between the different state space models that have been proposed, using what we consider to be proper definitions of state, controllability and observability and their relation to minimality of 2-D systems. We also represent new implementations of 2-D transfer functions using a minimal number of dynamic elements.

Martin Morf

Papers

Recursive Multichannel Maximum Entropy Spectral Estimation

Square-root algorithms for least-squares estimation

New inversion formulas for matrices classified in terms of their distance from Toeplitz matrices

Some new algorithms for recursive estimation in constant, linear, discrete-time systems

New results in 2-D systems theory, part I: 2-D polynomial matrices, factorization, and coprimeness