In the traditional total variation method

the removal of Poisson noise causes the “staircase effect” and image edge blurring in the plain area of the image. In reality

laser radar

satellite remote sensing

and medical imaging CT are based on the system of light quantum counting. The interference in image acquisition is basically subject to the Poisson distribution of quantum noise. How to effectively suppress the “staircase effect” and protect the edge of the image have thus become variational Poisson noise problems. To solve these problems

a new adaptive fractional-variation Poisson noise denoising model based on the traditional variational method is proposed.s The new model performs adaptive non-convex regularization based on the analysis of the Poisson noise distribution characteristics. Compared with the original model

the new non-convex regularization model can adjust the regularization coefficient adaptively according to the characteristics of regularization to different regions of the image; the image edge is therefore maintained. Regularization in the traditional total variational model involves the first-order discrete differential vector. Owing to the function characteristic of the bounded variation of the first-order differential vector

the “staircase effect” is easily caused in the plain area during denoising. To suppress the “staircase effect”

the new model uses the fractional discrete differential vector to combine the characteristics of image information and replaces the first-order discrete differential vector with the fractional discrete vector in the regularization. Given that the regularization of the new model is non-convex and the discrete differential is the fractional order differential vector

the traditional partial differential equation and the Chambolle projection algorithm cannot quickly and effectively obtain the numerical solution for the new model. For this reason

a more efficient numerical solution is proposed by combining the iterative method and the weighted primitive-dual method. Numerical results show that the new model is superior to the traditional total variational Poisson noise denoising model. The edge of the image is well protected

and the “staircase effect” is effectively suppressed. With the two classic images of Peppers and Lena as an example

the peak signal-to-noise ratio (PSNR) of the new model in the Peppers image is increased from 28.98 to 30.24 compared with the traditional model. The signal-to-noise ratio (SNR) is increased from 15.01 to 16.31

image structure similarity (SSIM) is increased from 0.77 to 0.87

and the mean square error of the image (MSE) is decreased from 82.24 to 61.52. In the Lena image

the PSNR of the new method is increased from 29.08 to 29.62

SNR is increased from 14.55 to 15.08

SSIM is increased from 0.78 to 0.83

and the MSE of the image is reduced from 80.37 to 70.97 compared with the traditional model. In addition

the numerical solution proposed in this study exhibits rapid convergence and low complexity compared with the traditional numerical solution. Similarly

with the classic Lena image as an example

the convergence time of the algorithm is reduced to 0.056 seconds compared with the convergence time of the partial differential equation

Chambolle projection

and other traditional numerical solutions (e.g.

0.5 and 0.1 seconds). Experimental results reveal the feasibility of the numerical method and model proposed in this study. The model and numerical solution are superior to traditional variants in terms of PSNR

SNR

MSE

and image visual effect. Numerical experimentation on several representative images shows that the new model and numerical solution possess good universality. The new model effectively suppresses the “staircase effect” and enhances the edge information of the image. It can effectively remove noise in radar and medical images. The fractional order in the new model is a fixed value. Obviously

different regions of the image use different orders of the fractional order to exert different effects. The effect of using a fixed value of the fractional order for the entire image could be subject to further improvement.