The subject of this dissertation is an electro-optical processing (EOP) concept which, in its basic configuration, computes a discrete linear transform such as Fourier, Laplace, Hilbert, etc., as well as convolutions and correlations. It accepts input signals through an incoherent light source, performs high speed analog multiplications via a two-dimensional array of apertures in a chrome mask on the surface of a charge-coupled device (CCD), shifts and integrates intermediate results within the CCD, and presents the transformed signal as a data stream from the output shift register of the CCD. The EOP concept is described in detail where both serial and parallel configurations are developed. It is seen to be an efficient computer of matrix-vector products, matrix-matrix products, and multichannel correlations. The inclusion of feedback and a changeable CCD mask yields an architecture for higher order matrix operations such as matrix inversion, solution of simultaneous equations, etc. A functional model of an EOP matrix-vector multiplier is presented which describes the accumulated effect of errors in system elements from the LED through the CCD. Also described is removal of error introduced by biasing required of input and mask modulation functions in order that they represent bipolar quantities. An EOP spectrum analyzer based upon direct implementation of the discrete Fourier transform (DFT) is described and use of a Kaiser-Bessel window function applied to the CCD mask is described as a solution to the "spectral leakage" problem caused by sharp discontinuities at each end of a normal window of sampled data. Finally, application of a parallel EOP configuration to the synthetic aperture radar (SAR) problem is offered. An architecture utilizing separate in-phase and quadrature EOP channels is described. The system shows potential for providing at least modest resolution SAR imagery with an economy of size, weight, and power consumption.

The problems of noise removal, and simultaneous noise removal and deblurring of imagery are common to many areas of science. An approach which allows for the unified treatment of both problems involves modeling imagery as a sample of a random process. Various nonstationary image models are explored in this context. Attention is directed to identifying the model parameters from imagery which has been corrupted by noise and possibly blur, and the use of the model to form an optimal reconstruction of the image. Throughout the work, emphasis is placed on both theoretical development and practical considerations involved in achieving this reconstruction. The results indicate that the use of nonstationary image models offers considerable improvement over traditional techniques.

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This paper proposes a metric to predict edge detection performance when applied to an image with noise. First, models of edges and edge detection linear operators are characterized by their spatial and Fourier domain properties. Second, additive uncorrelated noise on the operator is examined and a metric is developed using the image formation system modulation transfer function (MTF), expected noise power spectral density, and edge detector characterization as inputs. Thirdly, the problem of partially correlated noise is examined. A separate performance metric for simple thresholded operator outputs is proposed. Finally, several discrete edge detectors in noise are evaluated numerically. Both the metric based on signal to noise detector output, and based on thresholding probabilities were useful in predicting previously published performance results. This was true even for many nonlinear detectors based on the linear detectors evaluated here. The specification of a localization criteria was critical for comparisons between detectors.

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