Two Variational Models for Image Denoising Using Jacobian of Normals

Yan Zhai,Zhenkuan Pan,Weibo Wei

doi:10.1109/access.2021.3065662

Abstract

Variational models with second order regularizers can efficiently overcome the problems of staircasing effects caused by first order models. However, different types of second order regularizers may lead to different properties of feature preserving in restored images. In this paper, we show two variational models with second order regularizers. The first one is bounded Hessian model with Jacobian of normals, which uses bounded Jacobian of image intensity normals as regularizer, it is an extension of classical bounded Hessian (BH) model. The second one is total generalized variation model with Jacobian of normals, which is an extension to total generalized variation (TGV) model by replacing gradients in TGV with normals. The common objective is to improve feature preserving, such as edge, contrast and smoothness preservation. Additionally, their Alternating Direction Method of Multipliers (ADMM) are designed by introducing some proper auxiliary variables, Lagrange multipliers and penalty parameters to decompose the original models into some simple minimization sub-problems to solve. Extensive comparisons demonstrate that the proposed models are superior to the classical models with Hessian and TGV regularizers, especially in edge and corner preservation, smoothness, contrast enhancement. Moreover, the proposed models can be also extended to image inpainting, deblurring, and image enhancement.

Highlights

Variational models have been extensively used to different tasks of image processing and analysis [1,2,3], such as image deblurring, denoising [4], enhancement [5], inpainting [6], etc
EXPERIMENTAL RESULTS we set up some numerical experiments to demonstrate the merits of the proposed model through comparisons with the classical second order models including total Laplacian model (TL), bounded Hessian model (BH), mean curvature based model 1 and 2 (MC1, MC2), Euler’s elastic based model (EE), and total generalized variation (TGV) model
All these models are implemented using Alternating Direction Method of Multipliers (ADMM) algorithm and experimented according to the Fig. 1. Comparisons of these models are carried out objectively using peak signal-to-noise ratio (PSNR), structure similarity index map (SSIM) and root mean square error (RMSE)

Summary

Introduction

Variational models have been extensively used to different tasks of image processing and analysis [1,2,3], such as image deblurring, denoising [4], enhancement [5], inpainting [6], etc. The regularization terms in these models determine what kinds of image features can be preserved after restoration. The first order variational models have been widely used in many image processing problems [8], but staircasing phenomena usually exists in the results. Different second order regularizers have been designed successively to overcome the staircasing problem and preserve smoothness, contrast and corners for better image quality [9]. The second order derivatives of image intensity have different forms, which will lead to different properties of models. The normal based second order regularizers play an important role in geometric feature preserving

Results

Discussion

Conclusion