IMAGE DATA COMPRESSION AND RECONSTRUCTION BASED ON FREQUENCY DOMAIN CONSIDERATIONS AND PARTIAL DIFFERENTIAL EQUATION MODELS
CHEN, TING-CHUNG CHARLES
Doctor of Philosophy thesis
The image data compression and reconstruction problems are investigated in this dissertation, and new techniques for their solution are presented. Conventional image transform coding techniques are given a spatial domain interpretation. Based on this interpretation, an improvement using a larger transform size and an overlap-and-save scheme is presented for the Fourier transform which possesses simple spatial domain features. Next, spatial domain processing techniques based on frequency domain analysis are discussed. Two-dimensional digital filters are used to implement the compression and reconstruction scheme. McClellan's transformation and two fast approximation schemes are used to preserve the spectral properties of the image. To obtain a low mean-square-error, spatial constraints are added. Finally, a generalized spline interpolation approach based on partial differential equation image models is introduced. It is shown that this deterministic design is congruent to the stochastic minimum-mean-square-error estimation of the images given the decimated samples. Two implementation schemes, the cardinal spline filtering and the locally based B-spline fitting, are presented. The results are compared with the conventional Lagrange, cubic B-spline interpolation and the transform coding techniques. The various developments presented are demonstrated by computer simulations performed on a Genisco graphics display system supported by a PDP-11/55 computer.
Engineering, Electronics and Electrical