Denoising by singularity detection

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GaAs Implementation of FIR Filter

This thesis discusses the findings of the final year project involving Gallium Arsenide implementation of a triangular FIR filter to perform discrete wavelet transforms. The overall characteristics of Gallium Arsenide technology- its construction, behaviour and electrical charactersitics as they apply to VLSI technology - were investigated in this project. In depth understanding of its architecture is required to be able to understand the various design techniques employed. A comparison of Silicon and GaAs performance and other characteristics has also been made to fully justify the choice of this material for system implementation. A lot of research and active interest has gone into the field of image and video compression. Wavelet-based image transformation is one of the very efficient compression techniques used. An analysis of discrete wavelet transformations and the required triangular FIR filter was done to be able to produce a transform algorithm and the related filter architecture. Finally, the filter architecture was implemented as a VLSI design and layout. A variety of functional blocks required for the architecture were designed, tested and analysed. All these blocks were integrated to produce a model of a complete filter cell. The filter implementation was designed to be self-timed - without a system clock. Self-timed systems have considerable advantages over clocked architectures. Various design styles and handshaking mechanisms involved in designing a self-timed system were analysed and designed. There are many avenues still to explore. One of them is the VHDL analysis of filter architecture. Further development on this project would involve integration of higher-level logic and formation of a complete filter array

Wavelet-based digital image restoration

Digital image restoration is a fundamental image processing problem with underlying physical motivations. A digital imaging system is unable to generate a continuum of ideal pointwise measurements of the input scene. Instead, the acquired digital image is an array of measured values. Generally, algorithms can be developed to remove a significant part of the error associated with these measure image values provided a proper model of the image acquisition system is used as the basis for the algorithm development. The continuous/discrete/continuous (C/D/C) model has proven to be a better alternative compared to the relatively incomplete image acquisition models commonly used in image restoration. Because it is more comprehensive, the C/D/C model offers a basis for developing significantly better restoration filters. The C/D/C model uses Fourier domain techniques to account for system blur at the image formation level, for the potentially important effects of aliasing, for additive noise and for blur at the image reconstruction level.;This dissertation develops a wavelet-based representation for the C/D/C model, including a theoretical treatment of convolution and sampling. This wavelet-based C/D/C model representation is used to formulate the image restoration problem as a generalized least squares problem. The use of wavelets discretizes the image acquisition kernel, and in this way the image restoration problem is also discrete. The generalized least squares problem is solved using the singular value decomposition. Because image restoration is only meaningful in the presence of noise, restoration solutions must deal with the issue of noise amplification. In this dissertation the treatment of noise is addressed with a restoration parameter related to the singular values of the discrete image acquisition kernel. The restoration procedure is assessed using simulated scenes and real scenes with various degrees of smoothness, in the presence of noise. All these scenes are restoration-challenging because they have a considerable amount of spatial detail at small scale. An empirical procedure that provides a good initial guess of the restoration parameter is devised