Adaptive double-phase Rudin--Osher--Fatemi denoising model

Even though more than 30 years have passed since the seminal Rudin--Osher--Fatemi (ROF) paper on total variation (TV) denoising, it remains relevant, in particular in scientific applications such as astronomical imaging. However, it is known to suffer from artifacts such as the staircasing effect. Many variants of the model have been proposed with the aim of countering this. Recently, against the backdrop of immense research output on double-phase problems in the mathematical analysis community, a double-phase type integral functional, comprising of TV and a weighted term of quadratic growth, was suggested as a regularizer for image restoration. Here, we propose an adaptive variant of the ROF denoising model based on that regularizer. It is designed to reduce staircasing with respect to the classical ROF model, while preserving the edges of the image in a similar fashion. We implement the model and test its performance on synthetic and natural images over a range of noise levels. Compared to {established} models {with similar interpretability to ROF}, we observe an improved or similar performance in terms of similarity metrics SSIM, PSNR, {and LPIPS}, while the staircasing effect is visibly reduced.