abstract / Computer Science / Doctoral / Doctor of Philosophy

abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

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This dissertation describes the application of maximum entropy image restoration to envelope-detected ultrasonic sector scans. The maximum entropy restoration of the image of a point target (phantom) test object is shown to be superior to results obtained from the more familiar Wiener filter. The subsequent application of maximum entropy to an in-vivo clinical ultrasound image, however, illustrates the pitfalls associated with determining the relative merit of an ultrasonic image restoration technique from test object results alone. Since the resolution of sector scan images is substantially worse in the lateral (azimuthal) scan direction than the axial scan direction, the deconvolution filters described in this thesis were applied in the lateral direction only. The maximum entropy method is shown to have certain inherent advantages over linear frequency-domain techniques for the restoration of ultrasonic sector scan images. The positivity constraint inherent in the maximum entropy method is shown to produce restorations with substantially fewer oscillatory artifacts than those produced by Wiener filtering. In addition, the iterative nature of the maximum entropy algorithm is shown to be compatible with the restoration of the undersampled regions in the far field of sector scan images. The restoration of sector scan images is complicated by the spatially varying degradation associated with such images. A novel approach to the restoration of this class of image degradation is presented in this thesis. The widespread use of maximum entropy image restoration has been inhibited by the technique's demanding computational requirements. This problem can be alleviated by the use of high speed computer hardware, and the final chapters of this thesis describe the design and construction of a microcomputer-based array processor. The advantages inherent in the use of such hardware are demonstrated with reference to the maximum entropy restoration of ultrasonic images.

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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.

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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