Show simple item record

dc.contributor.authorChristou, Cameron 18:32:19 (GMT) 18:32:19 (GMT)
dc.description.abstractDithered quantization and noise shaping is well known in the audio community. The image processing community seems to be aware of this same theory only in bits and pieces, and frequently under conflicting terminology. This thesis attempts to show that dithered quantization of images is an extension of dithered quantization of audio signals to higher dimensions. Dithered quantization, or ``threshold modulation'', is investigated as a means of suppressing undesirable visual artifacts during the digital quantization, or requantization, of an image. Special attention is given to the statistical moments of the resulting error signal. Afterwards, noise shaping, or ``error diffusion'' methods are considered to try to improve on the dithered quantization technique. We also take time to develop the minimum-phase property for two-dimensional systems. This leads to a natural extension of Jensen's Inequality and the Hilbert transform relationship between the log-magnitude and phase of a two-dimensional system. We then describe how these developments are relevant to image processing.en
dc.publisherUniversity of Waterlooen
dc.subjectHilbert transformen
dc.subjectJensen's Inequalityen
dc.subjectNoise shapingen
dc.subjecterror momentsen
dc.titleOptimal Dither and Noise Shaping in Image Processingen
dc.typeMaster Thesisen
dc.subject.programApplied Mathematicsen Mathematicsen
uws-etd.degreeMaster of Mathematicsen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages