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

The extraction of sinusoids in white noise using least squares predictors has attracted a lot of attention in the past, mainly in the context of the adaptive line enhancer (ALE). However, very few results exist for the practical colored noise case or for the whitening performance of the predictors. We use a matrix formulation to derive the optimal least squares coefficients and frequency response of the D-step predictor or ALE for sinusoids (real or complex) in additive colored noise. Several cases are considered, and in particular, new formulas for the amplitude gain are obtained. In low-pass background noise, the amplitude gain of the sinusoids becomes essentially a monotonically increasing function of their frequency, and a decreasing function for high-pass noise. For the whitening application, signal-to-noise ratio (SNR) bounds of the output are derived when the input is a white signal plus a sinusoidal interference. We also give a state-space model and stochastic interpretations of our analysis of the D-step predictor, providing connections to other related areas. To enable filtering of nonstationary complex inputs, as well as multichannel and multiexperiment data, a complex vector version of the ladder algorithm is presented that can be used to implement the ALE, noise cancelling, and noise inversion for narrow-band interference rejection.

https://ieeexplore.ieee.org/iel6/29/26170/01163900.pdf

Enhancement of sinusoids in colored noise and the whitening performance of exact least squares predictors

Generalized Krein-Levinson Equations for Efficient Calculation of Fredholm Resolvents of Non-Displacement Kernels

Most present day computerized tomography (CT) systems are based on reconstruction algorithms that produce only approximate deterministic solutions of the image reconstruction problem. These algorithms yield reasonable results in cases of low measurement noise and regular measurement geometry, and are considered acceptable because they require far less computation and storage than more powerful algorithms that can yield near optimal results. However, the special geometry of the CT image reconstruction problem can be used to reduce by orders of magnitude the computation required for optimal reconstruction methods, such as the minimum variance estimator. These simplifications can make the minimum variance technique very competitive with well-known approximate techniques such as the algebraic reconstruction technique (ART) and convolution-back projection. The general minimum variance estimator for CT is first presented, and then a fast algorithm is described that uses Fourier transform techniques to implement the estimator for either fan beam or parallel beam geometries. The computational requirements of these estimators are examined and compared to other techniques. To allow further comparison with the commonly used convolution-back projection method, a representation of the fast algorithm is derived which allows its equivalent convolving function to be examined. Several examples are presented.

A Fast Implementation of a Minimum Variance Estimator for Computerized Tomography Image Reconstruction

: Ladder forms are probably the most promising canonical forms in estimation and system identification. Many record applications, such as in geophysical signal processing, high resolution ('maximum entropy') spectral estimation and speech encoding, justify the interest in these forms. They appear in many contexts, such as scattering and network theory and the theory of orthogonal polynomials. The state-space model ladder realizations are very closely related in (block) Schwarz matrix canonical forms, which generally appear in the context of stability analysis. In fact they are the natural 'stability canonical form' for (discrete-time) Lyapunov equations since the associated positive definite (covariance) matrices are diagonal resp. an identity. This fact leads also to close connections to square-root algorithms including the ones of Cholesky and Chandrasekhar type, since again Ladder forms are the natural canonical forms. In realization theory these forms are obtained via orthonormal state-space bases using Gram-Schmidt type procedures. Ladder forms have many other advantages, such as lowest computational complexity, good numerical behavior, stability 'by inspection' properties and relations to physical properties such as reflection or partial correlation coefficients, and perhaps absorption coefficients.

Ladder Forms Lin Estimation And System Identification

Simplifying the programming models is paramount to the success of reconfigurable computing. We apply the principles of object-oriented programming to the design of stream architectures for reconfigurable computing. The resulting tool, StReAm, is a domain specific compiler on top of the object-oriented module generation environment PAM-Blox. Combining module generation with a high-level programming tool in C++ gives the programmer the convenience to explore the flexibility of FPGAs on the arithmetic level and write the algorithms in the same language and environment.

Stream architectures consist of the pipelined dataflow graph mapped directly to hardware. Data streams through the implementation of the dataflow graphwithonly minimal control logic overhead. The main advantage of stream architectures is a clock-frequency equal to the data-rate leading to very low power consumption. We show a set of benchmarks from signal processing, encryption, image processing and 3D graphics in order to demonstrate the advantages of object-oriented programming of FPGAs.

Martin Morf

Papers

Enhancement of sinusoids in colored noise and the whitening performance of exact least squares predictors

Generalized Krein-Levinson Equations for Efficient Calculation of Fredholm Resolvents of Non-Displacement Kernels

A Fast Implementation of a Minimum Variance Estimator for Computerized Tomography Image Reconstruction

Ladder Forms Lin Estimation And System Identification

StReAm: Object-Oriented Programming of Stream Architectures Using PAM-Blox