- Title
- Canonical coordinates for transform coding of noisy sources
- Creator
- Schreier, Peter J.; Scharf, Louis L.
- Relation
- IEEE Transactions on Signal Processing Vol. 54, Issue 1, p. 235-243
- Publisher Link
- http://dx.doi.org/10.1109/TSP.2005.861085
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- journal article
- Date
- 2006
- Description
- Based on the additive white quantization noise model, linear transform coders are derived for Gaussian sources corrupted by noise. There are two alternative design objectives: minimizing the trace of the error correlation matrix and thus minimizing the mean-squared error, or minimizing the determinant of the error correlation matrix and thus maximizing information rate. It is shown that a solution to both problems is to first transform the noisy observations into canonical coordinates, quantize and apply a Wiener filter in this coordinate system, and then transform the result back to the original coordinates. Canonical coordinates are uncorrelated, and quantization and Wiener filtering are applied to each component independently. The type of canonical coordinate system depends on the design objective: Quantization in half-canonical coordinates minimizes the mean-squared error and quantization in full-canonical coordinates maximizes information rate. Finally, it is also demonstrated in this paper that majorization is the fundamental principle underlying proofs of optimal transform coding.
- Subject
- Gaussian sources; Wiener filter; additive white quantization noise model; canonical coordinates; error correlation matrix; mean-squared error method; noisy sources; quantization; transform coding
- Identifier
- uon:1204
- Identifier
- http://hdl.handle.net/1959.13/26904
- Identifier
- ISSN:1053-587X
- Rights
- Copyright © 2006 IEEE. Reprinted from IEEE Transactions on Signal Processing, Vol. 54, Issue 1, p. 235-243. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Newcastle's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
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