{"abstract":[{"lang":"eng","text":"Historically, transform coding of noisy sources has been performed by first estimating the message and then quantizing this estimate. We show that it is also optimum to first transform the noisy observations into canonical coordinates, quantize, apply a Wiener filter in this coordinate system, and then transform the result back to the original coordinates. Canonical coordinates are uncorrelated, and quantizing and Wiener filtering are applied to each component independently. Optimality of this approach can be proved assuming additive white quantization noise. Half canonical coordinates minimize the mean-squared error by minimizing the trace of the error covariance matrix and full canonical coordinates maximize information rate by minimizing the determinant of the error covariance matrix."}],"publication":"Proc.\\ IEEE Works.\\ Statistical Signal Proces.","page":"234–237","citation":{"ieee":"P. J. Schreier, L. L. Scharf, T. Hu, and S. D. Voran, “Canonical coordinates are the right coordinate system for transform coding of noisy sources,” in <i>Proc.\\ IEEE Works.\\ Statistical Signal Proces.</i>, 2003, pp. 234–237, doi: <a href=\"https://doi.org/10.1109/SSP.2003.1289387\">10.1109/SSP.2003.1289387</a>.","chicago":"Schreier, Peter J., Louis L. Scharf, Tianjian Hu, and Stephen D. Voran. “Canonical Coordinates Are the Right Coordinate System for Transform Coding of Noisy Sources.” In <i>Proc.\\ IEEE Works.\\ Statistical Signal Proces.</i>, 234–237, 2003. <a href=\"https://doi.org/10.1109/SSP.2003.1289387\">https://doi.org/10.1109/SSP.2003.1289387</a>.","apa":"Schreier, P. J., Scharf, L. L., Hu, T., &#38; Voran, S. D. (2003). Canonical coordinates are the right coordinate system for transform coding of noisy sources. <i>Proc.\\ IEEE Works.\\ Statistical Signal Proces.</i>, 234–237. <a href=\"https://doi.org/10.1109/SSP.2003.1289387\">https://doi.org/10.1109/SSP.2003.1289387</a>","short":"P.J. Schreier, L.L. Scharf, T. Hu, S.D. Voran, in: Proc.\\ IEEE Works.\\ Statistical Signal Proces., 2003, pp. 234–237.","ama":"Schreier PJ, Scharf LL, Hu T, Voran SD. Canonical coordinates are the right coordinate system for transform coding of noisy sources. In: <i>Proc.\\ IEEE Works.\\ Statistical Signal Proces.</i> ; 2003:234–237. doi:<a href=\"https://doi.org/10.1109/SSP.2003.1289387\">10.1109/SSP.2003.1289387</a>","bibtex":"@inproceedings{Schreier_Scharf_Hu_Voran_2003, title={Canonical coordinates are the right coordinate system for transform coding of noisy sources}, DOI={<a href=\"https://doi.org/10.1109/SSP.2003.1289387\">10.1109/SSP.2003.1289387</a>}, booktitle={Proc.\\ IEEE Works.\\ Statistical Signal Proces.}, author={Schreier, Peter J. and Scharf, Louis L. and Hu, Tianjian and Voran, Stephen D.}, year={2003}, pages={234–237} }","mla":"Schreier, Peter J., et al. “Canonical Coordinates Are the Right Coordinate System for Transform Coding of Noisy Sources.” <i>Proc.\\ IEEE Works.\\ Statistical Signal Proces.</i>, 2003, pp. 234–237, doi:<a href=\"https://doi.org/10.1109/SSP.2003.1289387\">10.1109/SSP.2003.1289387</a>."},"_id":"40901","status":"public","date_updated":"2023-01-30T11:52:49Z","doi":"10.1109/SSP.2003.1289387","date_created":"2023-01-30T11:52:09Z","title":"Canonical coordinates are the right coordinate system for transform coding of noisy sources","year":"2003","author":[{"last_name":"Schreier","full_name":"Schreier, Peter J.","first_name":"Peter J."},{"first_name":"Louis L.","last_name":"Scharf","full_name":"Scharf, Louis L."},{"first_name":"Tianjian","full_name":"Hu, Tianjian","last_name":"Hu"},{"first_name":"Stephen D.","last_name":"Voran","full_name":"Voran, Stephen D."}],"user_id":"43497","department":[{"_id":"263"}],"type":"conference"}