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文件名称:Wavelets, Ridgelets and Curvelets for Poisson Noise Removal
文件大小:5.68MB
文件格式:PDF
更新时间:2012-01-26 09:08:45
Curvelets, filtered Poisson process, multiscale
In order to denoise Poisson count data, we introduce
a variance stabilizing transform (VST) applied on a filtered
discrete Poisson process, yielding a near Gaussian process with
asymptotic constant variance. This new transform, which can be
deemed as an extension of the Anscombe transform to filtered
data, is simple, fast, and efficient in (very) low-count situations.We
combine this VST with the filter banks of wavelets, ridgelets and
curvelets, leading to multiscale VSTs (MS-VSTs) and nonlinear
decomposition schemes. By doing so, the noise-contaminated
coefficients of these MS-VST-modified transforms are asymptotically
normally distributed with known variances. A classical
hypothesis-testing framework is adopted to detect the significant
coefficients, and a sparsity-driven iterative scheme reconstructs
properly the final estimate. A range of examples show the power
of this MS-VST approach for recovering important structures of
various morphologies in (very) low-count images. These results
also demonstrate that the MS-VST approach is competitive relative
to many existing denoising methods.