Fast total variation minimizing image restoration under mixed Poisson-Gaussian noise

Abstract

Image acquisition in many biomedical imaging modalities is corrupted by Poisson noise followed by additive Gaussian noise. Maximum Likelihood Estimation (MLE) based restoration methods that use the exact Likelihood function for this mixed model with non-quadratic regularization are very few. In particular, while it has been demonstrated that total variation (TV) based regularization methods give better results, such methods that use exact Poisson-Gaussian Likelihood are slow. In this thesis, an ADMM (Alternating Direction Method of Multipliers) based fast algorithm was proposed for image restoration using exact Poisson-Gaussian Likelihood function and TV regularization. Speci fically, this thesis work describes a novel variable splitting approach that enables isolating the complexity in the exact log-likelihood functional from the image blurring operation, allowing a fast Newton-like iteration on the log-likelihood functional. This leads to a signi ficantly improved convergence rate of the overall ADMM iteration. Suffcient conditions for convergence of this algorithm are also derived as a part of the thesis. Expectation-Minimization based iterations were deployed to further exploit the proposed splitting approach. The effectiveness of the proposed methods was demonstrated using restoration examples. An extension to this method for super-resolved image reconstruction for structured illumination microscopy (SIM) was proposed. In SIM, extension of resolution beyond diffraction limit is achieved by illuminating the sample with a sinusoidal pattern. While known practical methods achieve reconstruction for SIM by modifying the measured data with sinusoidal modulation followed by a regularized multi-PSF deconvolution, the proposed approach achieves reconstruction by means of TV penalized MLE with exact likelihood composed of raw measured data.