A $\ell_2-\ell_p$ regulariser based model for Poisson noise removal using augmented Lagrangian method

TL;DR

This paper introduces a variational PDE model with an $-p$ regularizer for effective Poisson noise removal in blurred images, solved via augmented Lagrangian method, with demonstrated superior image quality metrics.

Contribution

It presents a novel $-p$ regularizer-based model for Poisson noise removal, including convergence analysis and comparison with existing methods.

Findings

Numerical simulations show improved SSIM, PSNR, and SNR over existing models.

The augmented Lagrangian method effectively solves the proposed minimization problem.

The model performs well on standard test images with Poisson noise and blur.

Abstract

In this article, we propose a variational PDE model using $\ell_2-\ell_p$ regulariser for removing Poisson noise in presence of blur. The proposed minimization problem is solved using augmented Lagrangian method. The convergence of the sequence of minimizers have been carried out. Numerical simulations on some standard test images have been shown. The numerical results are compared with that of a few models existed in literature in terms of image quality metric such as SSIM, PSNR and SNR.