Variance stabilization in Poisson image deblurring

Abstract

We consider the restoration of blurred images corrupted by Poisson noise using variance-stabilizing transformations (VST). Although VST are an established tool used extensively for denoising, their adoption in deconvolution problems is problematic because VST are necessarily nonlinear operators, and thus break the linear image-formation model typically adopted in deconvolution. We propose a deblurring framework where the image is 1) deconvolved by a linear regularized inverse filter, 2) transformed by VST into an image which can be treated as corrupted by strong spatially correlated noise with constant variance and known power spectrum, 3) denoised by a filter for additive colored Gaussian noise, 4) returned to the original range via inverse VST. We particularly analyze the stabilization of Poisson variates after linear filtering and characterize the noise power spectrum before and after application of VST. We present an efficient implementation of this original deblurring framework using the BM3D denoising filter, demonstrating state-of-the-art results which are especially appealing in low SNR imaging conditions.