UWSpace is currently experiencing technical difficulties resulting from its recent migration to a new version of its software. These technical issues are not affecting the submission and browse features of the site. UWaterloo community members may continue submitting items to UWSpace. We apologize for the inconvenience, and are actively working to resolve these technical issues.
 

Optimal Dither and Noise Shaping in Image Processing

Thumbnail Image

Files

thesis.pdf (7.14 MB)

Date

2008-08-20T18:32:19Z

Authors

Christou, Cameron

Journal Title

Journal ISSN

Volume Title

Publisher

University of Waterloo

Abstract

Dithered 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.

Description

Keywords

Hilbert transform, Jensen's Inequality, Dither, Noise shaping, quantization, error moments

LC Keywords

Citation

URI

http://hdl.handle.net/10012/3867

Collections

Theses
Applied Mathematics