Image denoising method based on variable exponential fractional‐integer‐order total variation and tight frame sparse regularization

Abstract

This study presents a variational image restoration algorithm based on variable exponential fractional‐order total variation (TV), variable exponential integer‐order TV and tight frame sparse regularization. The energy functional of this variational problem is composed of four parts: a fractional‐order TV regularization term with a variable exponent, an integer‐order TV regularization term with a variable exponent, a data fidelity term and a tight frame regularization term. The variable exponent is a function of the gradient information of the image. The first three parts of the energy functional is the smooth part, and the last part is the non‐smooth part. To minimize the smooth part, the optimization problem can be simply transformed into a gradient descent flow using the variational method. For the non‐smooth part, we use the soft‐thresholding method over the sparse framelet coefficients. As the combination of the fractional‐order derivative and integer‐order derivative, the variable exponent and the sparse regularisation, the proposed method can effectively remove noise of the image, protect the image boundary, and keep image texture details well. Experiments with simulated data and real data are provided to validate the effectiveness of proposed method. This method is robust to noise and is of some practical application value.

Enhanced Image Denoising with Diffusion Probability and Dictionary Learning Adaptation

“…Wang Y. and other researchers proposed to use variable exponential fractional reciprocal, integer reciprocal, and book writing regularization methods to achieve ID while preserving the texture details of the image. Research has shown that this method has strong robustness to noise [9]. Usui K. and other researchers used the denoising convolutional neural network (DnCNN) of convolutional neural network as a general CNN model and used it for transfer learning to denoise images.…”

MCMC algorithm based on Markov random field in image segmentation

“…Stepping into the 21st century, the development of computer science and technology is changing day by day, in which the processing and analysis of digital images have formed a unique scientific system [ 1 ]. In the processing and analysis of digital images, image segmentation (IS) is a key part [ 2 ]. However, effective image segmentation is not easy to realize in adaptive image processing due to insufficient a priori information and imaging noise [ 3 ].…”

A non-local image denoising method based on TV-L1 with variable exponents

“…To mitigate this issue, Li et al [5] proposed a TV model with variable exponents which can automatically adjust the norm of the gradient according to the features of different regions. With the expectation to remove noises and retain the details of the image simultaneously, the methods [6,7,8] selected the L1-norm as the regularization term for the edge of the image, and the L2-norm as the regularization term for the smooth regions, respectively. Although the adoption of variable exponents has reduced the staircasing effect of TVbased methods to a certain extent [5], their abilities to protect edge information are restrained by taking the L2-norm as the fidelity term.…”