Barry G. Sherlock

On the space of orthonormal wavelets

The space of orthonormal wavelets is described by a set of parameters for which a simple recurrence generates the coefficients for all orthonormal perfect-reconstruction FIR filters of arbitrary length. The space splits into two halves, each containing the time reverse of the others filters. A MATLAB implementation is given. This paper considers the generation of two-channel perfect reconstruction quadrature mirror filter banks corresponding to compactly supported orthonormal wavelets.

Optimum DCT quantization

The paper offers a solution to the problem of determining good quantization tables for use with the discrete cosine transform. Using the methods proposed, the designer of a system can choose a selection of test images and a coefficient weighting scenario, from which a quantization table can be produced, optimized for the choices made. The method is based on simulated annealing searches which the space of quantization tables to minimize some chosen measure.<<ETX>>

Windowed discrete cosine and sine transforms for shifting data

Abstract When processing a signal or an image using the discrete cosine transform (DCT) or discrete sine transform (DST), a typical approach is to extract a portion of the signal by windowing and then form the DCT or DST of the window contents. By shifting the window point by point over the signal, the entire signal may be processed. Previously, algorithms have been developed to “update” the DCT and DST simultaneously to reflect the modified window contents using less computation than directly evaluating the modified transform via standard fast transform algorithms. These algorithms are limited to a single point step between successive windows. In this paper, these results are extended to handle larger step sizes, i.e. an algorithm is developed to simultaneously update the DCT and DST to reflect inclusion of r , where 1⩽ r ⩽ N −1, additional data points and removal of r old points from the signal. Algorithms are derived for use with rectangular, split triangular (trapezoidal), Hanning, Hamming and Blackman windows, and implementations in the C language are given. Examples of applications where this algorithm would be useful include data communication where time constraints may not permit the immediate processing of every incoming data point, adaptive system identification, real-time analysis of financial market data, etc.

Robust control of an adaptive optical system

Abstract Most adaptive optical systems are based on a least-squares fit algorithm to optimize performance, and generally do not adequately address stability or uncertainty in the system. This paper describes the implementation of an H-infinity controller for an adaptive optical system, in order to optimize the closed-loop stability of the system.

Windowed discrete Fourier transform for shifting data

Abstract When processing a signal or image using the discrete Fourier transform (DFT), a typical approach is to extract a portion of the signal by windowing and then form the DFT of the window contents. By shifting the window point by point over the signal, the entire signal may be processed. The algorithms developed in this paper “update” the DFT to reflect the modified window contents, using less computation than directly evaluating the modified transform via the FFT algorithm. This reduces the computational order by a factor of log 2 N for both the 1-D and 2-D cases. Algorithms are derived for use with the boxcar, split triangular, Hanning, Hamming and Blackman windows, and implementations in the C language are given. The approach generalizes to piecewise linear and piecewise polynomial windows.

Transform domain technique for windowing the DCT and DST

In this paper, an algorithm is developed to apply Hann, Hamming, Blackman and related windows directly in the transform domain for the discrete cosine transform and discrete sine transform. These algorithms are useful in applications where windowing is required in order to minimize edge effects caused by implicit symmetries in the transform domain that are not replicated in the real-world data. Examples of such applications include data communication, adaptive system identification and filtering, real-time analysis of financial market data, etc. Software implementations in C language are also given.

Independently updating the DCT and DST for shifting windowed data

Abstract When processing a signal or an image using the Discrete Cosine Transform (DCT) or Discrete Sine Transform (DST), a typical approach is to extract a portion of the signal by windowing and then form the DCT or DST of the window contents. By shifting the window point by point over the signal, the entire signal may be processed. In this paper we develop algorithms to “update” the DCT and DST to reflect the modified window contents using less computation than by directly evaluating the modified transform via standard Fast Transform algorithms. Our algorithms constitute an improvement over previous DCT/ DST update algorithms because our approach establishes independence between the DCT and the DST: the algorithm for DCT makes use only of DCT terms, and similarly for DST. Algorithms are derived for use without windowing and with split-triangular, Hanning, Hamming and Blackman windows.

SIMULATED ANNEALING APPLIED TO OPTIMAL DCT QUANTIZATION

We present a method for determining optimum quantization tables for use in image compression systems which conform to the ISO/CCITT standard for Image Compression, also known as the Joint Photographic Experts Group (JPEG) standard1. An algorithm based on simulated annealing2 compresses and decompresses any collection of 8 by 8 pixel blocks, while searching the space of 8 by 8 quantization tables for optimum fidelity according to some chosen measure. A composite cost function maintains a predefined compression ratio while minimizing the RMS error in the decoded image compared to the original. The process can be carried out on a raw image, or greater weight can be given to a selected range of DCT coefficients on the basis of psychophysical considerations3. The results of applying the methods to the intensity (y) components of three JPEG test images are presented. In all cases improved fidelity as measured by RMS error is obtained compared to the quantization table suggested in the JPEG standard. Significantly, the quantization tables obtained for one image most often provide smaller error when applied to other images than does the table suggested with the JPEG standard. An unexpected result when using pre-emphasized images suggests that the psychophysical assumptions underlying the suggested JPEG table may be oversimplified. By applying the method to blocks selected from a variety of images, improved quantization tables can be found for images in general, including color.

A target tracking algorithm that reduces designation time for laser guided weapons

We propose a new approach for laser guided weapon guidance that minimizes the total active laser target designation time. The weapon makes use of inertial or GPS guidance within a Kalman filtering framework, and maintains covariance information indicating the uncertainty of its knowledge of the weapon-to-target vector. At any time, the missile needs to be sure that it can navigate to any point within the area around the target that is described by this covariance. Therefore, at each moment during the flight, there exists a covariance threshold above which the weapon cannot guarantee its ability to navigate to the target. This threshold will decrease with time as the weapon-to-target distance decreases. In our proposed approach, when the threshold is exceeded, the weapon requests a brief laser designation of the target. The laser designation provides an accurate measurement of the bearing of the target with respect to the missile, and this is used to improve the estimate of the weapon-to-target vector. In turn, this can be fed back into the Kalman filter to improve the internal state estimate. By minimizing laser designation time, this approach reduces the chance of compromise of the designation agent, and of the fact that targeting is taking place. It also achieves the benefit of improving the accuracy of the underlying inertial or other navigational system, or alternatively the estimate of absolute target position.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Computer Enhancement and Modeling of Fingerprint Images

The chapter discusses computer enhancement of fingerprint images, as well as the mathematical modeling of fingerprint ridge structure.