As an important, challenging, and difficult problem in image processing, multiplicative noise removal (MNR) has attracted great attention. To this end, many variational methods have been effectively proposed in the past few decades. Among these variational methods, total variation (TV) and its higher-order extensions are very effective, where the former can preserve sharp edges but cause some undesirable staircase effects and the latter can better reduce the staircase effects but sometimes smooth the image details. To overcome the drawbacks while taking full use of their merits, the authors propose a novel hybrid higher-order TV regularisation model for MNR, in which the novelty of the proposed model consists of combining the image prior information of first-order and second-order derivatives to propose a novel higher-order regulariser, named as hybrid higher-order TV (HHTV). More specifically, a more preferable equivalent formulation of HHTV is derived. Then, they use the derived equivalent formulation to design an efficient alternating iterative algorithm to solve the proposed model. Finally, the experimental results demonstrate that the proposed HHTV method outperforms several state-of-the-art methods in terms of image quality and convergence speed.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-ipr.2018.5930

Hybrid higher-order total variation model for multiplicative noise removal

Image deblurring based on fractional-order total variation and total generalized variation

Efficient SAV-Based Algorithms for Image Multiplicative Denoising with a Second Fundamental Form Regularizer

In this study, a novel normal curvature-induced variational model which involves a higher-order regulariser based on the normal curvature prior information of image surface is proposed for image restoration. Furthermore, the authors derive a preferably equivalent formulation for the proposed normal curvature-induced higher-order regulariser. Then, they design an efficient algorithm to solve the proposed model by using the famous alternating direction method of multipliers technique. Finally, they assess the performance of the proposed method on both natural images and biomedical cell images by comparing it with the famous fast total variation (TV) method, fractional-order TV method and Hessian-nuclear-norm regularisation method. Specifically, the proposed method can achieve better and more balanced results in terms of peak-signal-to-noise ratio, convergence rate and restoration quality.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-ipr.2017.0603

Normal curvature-induced variational model for image restoration

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Normal curvature-induced variational model for image restoration