Image processing techniques find applications in many areas, chief among which are image enhancement, pattern recognition, and efficient picture coding. Some aspects of image processing are discussed--specifically: the mathematical operations one is likely to encounter, and ways of implementing them by optics and on digital computers; image description; and image quality evaluation. Many old results are reviewed, some new ones presented, and several open questions are posed.

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

Data flow is a natural paradigm for describing DSP applications for concurrent implementation on parallel hardware. Data flow programs for signal processing are directed graphs where each node represents a function and each arc represents a signal path. Synchronous data flow (SDF) is a special case of data flow (either atomic or large grain) in which the number of data samples produced or consumed by each node on each invocation is specified a priori. Nodes can be scheduled statically (at compile time) onto single or parallel programmable processors so the run-time overhead usually associated with data flow evaporates. Multiple sample rates within the same system are easily and naturally handled. Conditions for correctness of SDF graph are explained and scheduling algorithms are described for homogeneous parallel processors sharing memory. A preliminary SDF software system for automatically generating assembly language code for DSP microcomputers is described. Two new efficiency techniques are introduced, static buffering and an extension to SDF to efficiently implement conditionals.

Synchronous data flow

Purpose: We sought to describe and validate an automated image registration method(AIR 3.0) based on matching of voxel intensities. Method: Different cost functions, different minimization methods, and various sampling, smoothing, and editing strategies were compared. Internal consistency measures were used to place limits on registration accuracy for MRI data, and absolute accuracy was measured using a brain phantom for PET data. Results: All strategies were consistent with subvoxel accuracy for intrasubject, intramodality registration. Estimated accuracy of registration of structural MRI images was in the 75 to 150 µm range. Sparse data sampling strategies reduced registration times to minutes with only modest loss of accuracy. Conclusion: The registration algorithm described is a robust and flexible tool that can be used to address a variety of image registration problems. Registration strategies can be tailored to meet different needs by optimizing tradeoffs between speed and accuracy.

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Automated Image Registration: I. General Methods and Intrasubject, Intramodality Validation

The first edition of this book has enjoyed a gratifying existence. 1s sued in 1965, it found its intended place as a research reference and as a graduate-Ievel text. Research laboratories and universities reported broad use. Published reviews-some twenty-five in number-were universally kind. Subsequently the book was translated and published in Russian (Svyaz; Moscow, 1968) and Spanish (Gredos, S.A.; Madrid, 1972). Copies of the first edition have been exhausted for several years, but demand for the material continues. At the behest of the publisher, and with the encouragement of numerous colleagues, a second edition was begun in 1970. The aim was to retain the original format, but to expand the content, especially in the areas of digital communications and com puter techniques for speech signal processing. As before, the intended audience is the graduate-Ievel engineer and physicist, but the psycho physicist, phonetician, speech scientist and linguist should find material of interest."

Speech Analysis, Synthesis and Perception

A digital frequency synthesizer has been designed and constructed based on generating digital samples of \exp [j(2^{\pi}nk/N)] at time nT . The real and imaginary parts of this exponential form samples of quadrature sinusoids where the frequency index k is allowed to vary (-N/4) \leq K . The digital samples drive digital to analog converters followed by low-pass interpolating filters to produce analog sinusoids. The method is superior to digital difference equations with poles on the unit circle since the noise or numerical inaccuracy remains bounded. The digital technique used consists of factoring the exponential into two table look-ups from an efficiently organized small READ-ONLY memory table and performing a complex multiply to produce the real and imaginary components. A small array multiplier efficiently organized performs the multiplications. The technique lends itself to the production of phase coherent or phase controlled sinusoids because of the indexing arrangement used. In addition finer frequency steps than the READ-ONLY memory allows are available by expanding the indexing register at no increase in inaccuracy.

A digital frequency synthesizer

Digital processing of signals

A computational algorithm for numerically evaluating the z -transform of a sequence of N samples is discussed. This algorithm has been named the chirp z -transform (CZT) algorithm. Using the CZT algorithm one can efficiently evaluate the z -transform at M points in the z -plane which lie on circular or spiral contours beginning at any arbitrary point in the z -plane. The angular spacing of the points is an arbitrary constant, and M and N are arbitrary integers. The algorithm is based on the fact that the values of the z -transform on a circular or spiral contour can be expressed as a discrete convolution. Thus one can use well-known high-speed convolution techniques to evaluate the transform efficiently. For M and N moderately large, the computation time is roughly proportional to (N+M) \log_{2}(N+M) as opposed to being proportional to N . M for direct evaluation of the z -transform at M points.

/pdf/the-chirp-z-transform-algorithm-2bu061tl7o.pdf

The chirp z-transform algorithm

We discuss a computational algorithm for numerically evaluating the z-transform of a sequence of N samples. This algorithm has been named the chirp z-transform algorithm. Using this algorithm one can efficiently evaluate the z-transform at M points in the z-plane which lie on circular or spiral contours beginning at any arbitrary point in the z-plane. The angular spacing of the points is an arbitrary constant; M and N are arbitrary integers. The algorithm is based on the fact that the values of the z-transform on a circular or spiral contour can be expressed as a discrete convolution. Thus one can use well-known high-speed convolution techniques to evaluate the transform efficiently. For M and N moderately large, the computation time is roughly proportional to (N + M) log 2 (N + M) as opposed to being proportional to N · M for direct evaluation of the z-transform at M points. Applications discussed include: enhancement of poles in spectral analysis, high resolution narrow-band frequency analysis, interpolation of band-limited waveforms, and the conversion of a base 2 fast Fourier transform program into an arbitrary radix fast Fourier transform program.

The chirp z-transform algorithm and its application

Digital filtering is the process of spectrum shaping using digital components as the basic elements Increasing speed and decreasing size and cost of digital components make it likely that digital filtering, already used extensively in the computer simulation of analog filters, will perform, in real-time devices, the functions which are now performed almost exclusively by analog components In this paper, using the z-transform calculus, several digital filter design techniques are reviewed, and new ones are presented One technique can be used to design a digital filter whose impulse response is like that of a given analog filter; other techniques are suitable for the design of a digital filter meeting frequency response criteria Another technique yields digital filters with linear phase, specified frequency response, and controlled impulse response duration The effect of digital arithmetic on the behavior of digital filters is also considered

Charles M. Rader

Papers

A digital frequency synthesizer

Digital processing of signals

The chirp z-transform algorithm

The chirp z-transform algorithm and its application

Digital filter design techniques in the frequency domain