The purpose of this paper is to examine properties of convex sets in linear topological spaces with special emphasis on compact convex sets.

by Ngai-ching Wong. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 197-201.

by Ma Mang Fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1989. / Bibliography: leaf 77.

When one takes an x-ray, one learns how much material is along the line between the x-ray source and the x-ray sensor. The goal of tomography is to learn what one can about an object, by knowing how much material is on a collection of lines or rays passing through that object. Mathematically, this is a collection of line integrals of density function of the object. In this paper, we provide and prove reconstructions for a class of convex objects of uniform density using x-rays from three point sources.

Typescript (Photocopy) Bibliography: leaf 75.

This thesis examines the problem of reconstructing multiple discrete 2D objects, represented by a set of cells arranged in an m × n grid, from their projections. The objects being constructed are disjoint, hv-convex polyominoes, each of which has a separate colour. The main results presented here are two algorithms for unordered C-colour reconstruction that have time complexities of O(C^2n^{2C +1}m^{2C +1}) and O(C^2 min(n^{2C}, m^{2C})nm), an ordered C-colour reconstruction algorithm that is O(Cmin(n^{2C}, m^{2C})nm), and an NP-completeness proof when the number of colours is unbounded.

This thesis examines the problem of reconstructing multiple discrete 2D objects, represented by a set of cells arranged in an m × n grid, from their projections. The objects being constructed are disjoint, hv-convex polyominoes, each of which has a separate colour. The main results presented here are two algorithms for unordered C-colour reconstruction that have time complexities of O(C^2n^{2C +1}m^{2C +1}) and O(C^2 min(n^{2C}, m^{2C})nm), an ordered C-colour reconstruction algorithm that is O(Cmin(n^{2C}, m^{2C})nm), and an NP-completeness proof when the number of colours is unbounded.

In this thesis, the basic theory is convex optimization theory[1]. And we study the problem about how to transfer to convex optimization problem from the filter design problem. So that we can guarantee the solution is the globally optimized solution. As we get the filter coefficients, we quantize them, then to reduce the quantization bits of the filter coefficients by using the algorithm[2]. At last, we try to change the sequence of quantization, and compared the result with the result of the method[2].

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