Lattice quantization error for redundant representations

Sergiy Borodachov; Yang Wang

doi:10.1117/12.826755

4 September 2009 Lattice quantization error for redundant representations

Sergiy Borodachov, Yang Wang

Proceedings Volume 7446, Wavelets XIII; 74460N (2009) https://doi.org/10.1117/12.826755
Event: SPIE Optical Engineering + Applications, 2009, San Diego, California, United States

Abstract

Redundant systems such as frames are often used to represent a signal for error correction, denoising and general robustness. In the digital domain quantization needs to be performed. Given the redundancy, the distribution of quantization errors can be rather complex. In this paper we study quantization error for a signal X in R^d represented by a frame using a lattice quantizer. We characterize the asymptotic distribution of the quantization error as the cell size of the lattice goes to zero. We apply these results to get the necessary and sufficient conditions for the White Noise Hypothesis to hold asymptotically in the case of the pulse-code modulation scheme. This is an abbreviated version of a paper that will appear elsewhere in a regular refereed journal.

Citation Download Citation

Sergiy Borodachov and Yang Wang "Lattice quantization error for redundant representations", Proc. SPIE 7446, Wavelets XIII, 74460N (4 September 2009); https://doi.org/10.1117/12.826755

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