An Orthogonality Principle for Select-Maximum Estimation of Exponential Variables

It was recently proposed to encode the one-sided exponential source X via K parallel channels, Y1, ..., YK , such that the error signals X - Yi, i = 1,...,K, are one-sided exponential and mutually independent given X. Moreover, it was shown that the optimal estimator \hat{Y} of the source X with respect to the one-sided error criterion, is simply given by the maximum of the outputs, i.e., \hat{Y} = max{Y1,..., YK}. In this paper, we show that the distribution of the resulting estimation error X - \hat{Y} , is equivalent to that of the optimum noise in the backward test-channel of the one-sided exponential source, i.e., it is one-sided exponentially distributed and statistically independent of the joint output Y1,...,YK.Comment: 5 pages. Submitted to ISI

Rate scalable image compression in the wavelet domain

This thesis explores image compression in the wavelet transform domain. This the- sis considers progressive compression based on bit plane coding. The rst part of the thesis investigates the scalar quantisation technique for multidimensional images such as colour and multispectral image. Embedded coders such as SPIHT and SPECK are known to be very simple and e cient algorithms for compression in the wavelet do- main. However, these algorithms require the use of lists to keep track of partitioning processes, and such lists involve high memory requirement during the encoding process. A listless approach has been proposed for multispectral image compression in order to reduce the working memory required. The earlier listless coders are extended into three dimensional coder so that redundancy in the spectral domain can be exploited. Listless implementation requires a xed memory of 4 bits per pixel to represent the state of each transformed coe cient. The state is updated during coding based on test of sig- ni cance. Spectral redundancies are exploited to improve the performance of the coder by modifying its scanning rules and the initial marker/state. For colour images, this is done by conducting a joint the signi cant test for the chrominance planes. In this way, the similarities between the chrominance planes can be exploited during the cod- ing process. Fixed memory listless methods that exploit spectral redundancies enable e cient coding while maintaining rate scalability and progressive transmission. The second part of the thesis addresses image compression using directional filters in the wavelet domain. A directional lter is expected to improve the retention of edge and curve information during compression. Current implementations of hybrid wavelet and directional (HWD) lters improve the contour representation of compressed images, but su er from the pseudo-Gibbs phenomenon in the smooth regions of the images. A di erent approach to directional lters in the wavelet transforms is proposed to remove such artifacts while maintaining the ability to preserve contours and texture. Imple- mentation with grayscale images shows improvements in terms of distortion rates and the structural similarity, especially in images with contours. The proposed transform manages to preserve the directional capability without pseudo-Gibbs artifacts and at the same time reduces the complexity of wavelet transform with directional lter. Fur-ther investigation to colour images shows the transform able to preserve texture and curve.EThOS - Electronic Theses Online ServiceGBUnited Kingdo