Technical Program

Paper Detail

Paper:	IMDSP-L4.3
Session:	Restoration and Enhancement
Time:	Wednesday, May 17, 10:40 - 11:00
Presentation:	Lecture
Topic:	Image and Multidimensional Signal Processing: Restoration and Enhancement
Title:	Multi-scale variance stabilizing transform for multi-dimensional Poisson count image denoising
Authors:	Bo Zhang, Institut Pasteur, France; Jalal Fadili, GREYC UMR 6072 CNRS, France; Jean-Luc Starck, DAPNIA / SEDI-SAP, France
Abstract:	We propose in this paper a Multi-Scale Variance Stabilizing Transform (MSVST) for approximately Gaussianizing and stabilizing the variance of a sequence of independent Poisson random variables (RVs) filtered by a low-pass linear filter. This approach is shown to be fast, very well adapted to extremely low-count situations and easily applicable to any dimensional data. It is shown that the RV transformed using Anscombe VST can be reasonably considered as stabilized for an intensity $\lambda \gtrsim 10$, using Fisz VST for $\lambda \gtrsim 1$ and using our VST (after low-pass filtering) for $\lambda \gtrsim 0.1$. We then use the MSVST technique to stabilize the detail coefficients of the Isotropic Undecimated Wavelet Transform (IUWT) of multi-dimensional Poisson count data. We use a hypothesis testing framework in the wavelet domain to denoise the Gaussianized and stabilized coefficients, and then apply the inverse MSVST-IUWT to get the estimated intensity image underlying the Poisson data. Finally, potential applicability of our approach is illustrated on an astronomical example where isotropic structures must be recovered.