Directional TGV-based image restoration under Poisson noise

TL;DR

This paper extends the Directional Total Generalized Variation (DTGV) method to restore images corrupted by Poisson noise, incorporating a texture direction identification and an efficient ADMM algorithm, showing promising results on real and phantom images.

Contribution

It introduces a Poisson noise-specific DTGV regularization with a new texture direction identification technique and an efficient ADMM-based solution.

Findings

Effective restoration of Poisson noisy images demonstrated

Improved texture direction estimation enhances results

Algorithm converges reliably with low computational cost

Abstract

We are interested in the restoration of noisy and blurry images where the texture mainly follows a single direction (i.e., directional images). Problems of this type arise, for example, in microscopy or computed tomography for carbon or glass fibres. In order to deal with these problems, the Directional Total Generalized Variation (DTGV) was developed by Kongskov et al. in 2017 and 2019, in the case of impulse and Gaussian noise. In this article we focus on images corrupted by Poisson noise, extending the DTGV regularization to image restoration models where the data fitting term is the generalized Kullback-Leibler divergence. We also propose a technique for the identification of the main texture direction, which improves upon the techniques used in the aforementioned work about DTGV. We solve the problem by an ADMM algorithm with proven convergence and subproblems that can be solved exactly at a low computational cost. Numerical results on both phantom and real images demonstrate the effectiveness of our approach.