Poisson denoising on the sphere

J. Schmitt; J. L. Starck; J. Fadili; I. Grenier; J. M. Casandjian

doi:10.1117/12.824446

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4 September 2009 Poisson denoising on the sphere

J. Schmitt, J. L. Starck, J. Fadili, I. Grenier, J. M. Casandjian

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Proceedings Volume 7446, Wavelets XIII; 74461A (2009) https://doi.org/10.1117/12.824446
Event: SPIE Optical Engineering + Applications, 2009, San Diego, California, United States

Abstract

In the scope of the Fermi mission, Poisson noise removal should improve data quality and make source detection easier. This paper presents a method for Poisson data denoising on sphere, called Multi-Scale Variance Stabilizing Transform on Sphere (MS-VSTS). This method is based on a Variance Stabilizing Transform (VST), a transform which aims to stabilize a Poisson data set such that each stabilized sample has an (asymptotically) constant variance. In addition, for the VST used in the method, the transformed data are asymptotically Gaussian. Thus, MS-VSTS consists in decomposing the data into a sparse multi-scale dictionary (wavelets, curvelets, ridgelets...), and then applying a VST on the coefficients in order to get quasi-Gaussian stabilized coefficients. In this present article, the used multi-scale transform is the Isotropic Undecimated Wavelet Transform. Then, hypothesis tests are made to detect significant coefficients, and the denoised image is reconstructed with an iterative method based on Hybrid Steepest Descent (HST). The method is tested on simulated Fermi data.

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J. Schmitt, J. L. Starck, J. Fadili, I. Grenier, and J. M. Casandjian "Poisson denoising on the sphere", Proc. SPIE 7446, Wavelets XIII, 74461A (4 September 2009); https://doi.org/10.1117/12.824446

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