2 February 2009 Wavelet-based Poisson rate estimation using the Skellam distribution
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Abstract
Owing to the stochastic nature of discrete processes such as photon counts in imaging, real-world data measurements often exhibit heteroscedastic behavior. In particular, time series components and other measurements may frequently be assumed to be non-iid Poisson random variables, whose rate parameter is proportional to the underlying signal of interest-witness literature in digital communications, signal processing, astronomy, and magnetic resonance imaging applications. In this work, we show that certain wavelet and filterbank transform coefficients corresponding to vector-valued measurements of this type are distributed as sums and differences of independent Poisson counts, taking the so-called Skellam distribution. While exact estimates rarely admit analytical forms, we present Skellam mean estimators under both frequentist and Bayes models, as well as computationally efficient approximations and shrinkage rules, that may be interpreted as Poisson rate estimation method performed in certain wavelet/filterbank transform domains. This indicates a promising potential approach for denoising of Poisson counts in the above-mentioned applications.
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Keigo Hirakawa, Farhan Baqai, Patrick J. Wolfe, "Wavelet-based Poisson rate estimation using the Skellam distribution", Proc. SPIE 7246, Computational Imaging VII, 72460R (2 February 2009); doi: 10.1117/12.815487; https://doi.org/10.1117/12.815487
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