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Nonparametric Estimation of Intensity Maps Using Haar Wavelets and Poisson Noise Characteristics

  • Authors: Eric D. Kolaczyk and David D. Dixon

Kolaczyk & Dixon 2000 The Astrophysical Journal 534 490.

  • Provider: AAS Journals

Caption: Fig. 2.

(a) Simulated data based on the distribution in Fig. 1, with a background level of 0.1 counts pixel−1. ﹩\mathrm{MSE}\,=0.1﹩. (b) TIPSH denoised version of (a), using hard thresholding and the calibrated thresholds of eq. (3). ﹩\mathrm{MSE}\,=3.9\times 10^{-5}﹩. (c) Same as (b), using soft‐threshold nonlinearity. ﹩\mathrm{MSE}\,=5.6\times 10^{-5}﹩. (d) Result from the "standard" approach of applying the VST, denoising via hard thresholding as for unit additive white noise and inverting the VST. Note that count levels are distorted compared with (b) and (c), e.g., the background is significantly below the expected level of 0.1 counts pixel−1. ﹩\mathrm{MSE}\,=1.1\times 10^{-3}﹩.

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