Directional TGV-based image restoration under Poisson noise
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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) has been presented in [R.D. Kongskov Y. Dong, SSVM 2017, LNCS 10302, 2017; R.D. Kongskov, Y. Dong K. Knudsen, BIT 59, 2019] in the case of impulse and Gaussian noise. In this work 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 aformentioned articles. 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.
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