Poisson image denoising using fast discrete curvelet transform and wave atom

In this paper, we propose a strategy to combine fast discrete curvelet transform (FDCT) and wave atom (WA) with multiscale variance stabilizing transform (MS-VST); our objective is to develop algorithms for Poisson noise removal from images. Applying variance stabilizing transform (VST) on a Poisson noisy image results in a nearly Gaussian distributed image. The noise removal can be subsequently done assuming a Gaussian noise model. MS-VST has been recently proposed in the literature (i) to improve the denoising performance of Anscombe's VST at low intensity regions of the image and (ii) to facilitate the use of multiscale-multidirectional transforms like the curvelet transform for Poisson image denoising. Since the MS-VST has been implemented in the space-domain, it is not clear how it can be extended to FDCT and WA, which are incidentally implemented in the frequency-domain. We propose a simple strategy to achieve this without increasing the computational complexity. We also extend our approach to handle the recently developed mirror-extended versions of FDCT and WA. We have carried out simulations to validate the performance of the proposed approach. The results demonstrate that the MS-VST combined with FDCT and WA are promising candidates for Poisson denoising. (C) 2012 Elsevier B.V. All rights reserved.