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Proceedings Paper

Multiplicative multiscale image decompositions: analysis and modeling
Author(s): Justin K. Romberg; Rudolf H. Riedi; Hyeokho Choi; Richard G. Baraniuk
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Paper Abstract

Multiscale processing, in particular using the wavelet transform, has emerged as an incredibly effective paradigm for signal processing and analysis. In this paper, we discuss a close relative of the Haar wavelet transform, the multiscale multiplicative decomposition. While the Haar transform captures the differences between signal approximations at different scales, the multiplicative decomposition captures their ratio. The multiplicative decomposition has many of the properties that have made wavelets so successful. Most notably, the multipliers are a sparse representative for smooth signals, they have a dependency structure similar to wavelet coefficients, and they can be calculated efficiently. The multiplicative decomposition is also a more natural signal representation than the wavelet transform for some problems. For example, it is extremely easy to incorporate positivity constraints into multiplier domain processing. In addition, there is a close relationship between the multiplicative decomposition and the Poisson process; a fact that has been exploited in the field of photon-limited imaging. In this paper, we will show that the multiplicative decomposition is also closely tied with the Kullback-Leibler distance between two signals. This allows us to derive an n-term KL approximation scheme using the multiplicative decomposition.

Paper Details

Date Published: 4 December 2000
PDF: 12 pages
Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408660
Show Author Affiliations
Justin K. Romberg, Rice Univ. (United States)
Rudolf H. Riedi, Rice Univ. (United States)
Hyeokho Choi, Rice Univ. (United States)
Richard G. Baraniuk, Rice Univ. (United States)

Published in SPIE Proceedings Vol. 4119:
Wavelet Applications in Signal and Image Processing VIII
Akram Aldroubi; Andrew F. Laine; Michael A. Unser, Editor(s)

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