Sampling and Digital Representation of Waveforms and Images

作     者：Oakley, John Peter 

作者单位：Brunel University London 

学位级别：博士

授予年度：1987年

摘      要：This thesis is concerned with methods for Digital Signal Processing (DSP) with particular emphasis on image processing. The interest is primarily in the sampling and reconstruction of continuous temporal and spatial functions. Any continuous waveform may be accurately described by a sequence of sample values provided that enough samples are taken. However, in areas such as digital image interpretation, the large size of the data set (typically 512 by 512 pixels) causes problems and so oversampling should be avoided. The Shannon sampling theorem gives the conditions for exact reconstruction of a continuous waveform from sample values but these conditions are not met in practical systems. An alternative view of sampling is presented here. This takes the form of a mathematical model for DSP systems in which the input and output functions are modeled as Banach function spaces. The action of the DSP system is that of an integral operator which maps the input space to the output space. The correctness of the DSP system is assessed with two metrics. The first metric, called the Accuracy metric, deals with the closeness of the DSP system to a continuous convolution operator. The second metric, called the Isometric Variance metric, quantifies the shift-variance of the system. The implications of the model for a Hilbert space input and two different output spaces are examined. Three applications of the model in image processing are considered. The first application is in the design of image reconstruction algorithms. The model is used to derive reconstruction algorithms which are matched to the spatial characteristics of the image sensor. The second application is in image storage using local basis functions. The model is used to assess the suitability of basis functions and to design sampling algorithms. The third application is in formulating edge detection operators for computer vision systems. A microcomputer-based image processing system is used together with a dedicated