The total variation (TV) denoising model is unideal for maintaining the weak edge and weak textural detail of images

even though this model has satisfied the noise reduction performance. Adaptive fractional TV (AFTV) algorithm was presented to identify the texture and non-texture areas in an image based on local image information. The soft threshold value in an adaptive method was also calculated. Thus

the weak edges and weak texture details in the noise image can be preserved substantially better than the traditional TV algorithm could. However

the retaining effect of the weak edge and weak texture detail deteriorates as the noise increases

thereby substantially causing an evident staircase effect. To address this problem

the current study proposes a novel fractional TV denoising algorithm by applying fractional differential theory combined with the TV and characteristics of the residual image. A fractional-order TV model is proposed to substitute for the original first-order TV model. The image is divided into texture and flat areas based on the accurate local variance of the residual image

thereby enabling the adaptive selection of the fidelity item parameter to become considerably reasonable. Consequently

the denoising performance is improved

particularly in processing images with high noise. To verify the denoising effect and texture-preserving capability

experiments on images with three different noise levels are performed using the proposed algorithm and with the TV and AFTV models. In these experiments

the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) are adopted as evaluation indexes. For example

Gaussian noise with a standard deviation of 30 is added in the experiment on the classic image of the cameraman

which is acquired from a standard image library. This experiment shows that the distribution of the texture detail and noise area in the residual image is disorganized and inaccurate by using the AFTV algorithm but more reasonable and refined using the proposed model. Additional experiments are conducted using standard and nature images

including Lena

Barbara

and Rock

which are contaminated by Gaussian noise

salt-and-pepper noise

and Poisson noise with different noise levels. On the one hand

for the Gaussian-noise image

the proposed algorithm adds the Gaussian noise with a series of standard deviations of 10

20

30

40

and 50 to the test images. Experimental results show that the PSNR value obtained by the proposed algorithm increases by 2.72 dB more than that of the TV model and by 1.38 dB more than that of the AFTV model. Simultaneously

the SSIM value obtained by the proposed algorithm is 0.047 more than that of the TV model and 0.020 more than that of the AFTV model. On the other hand

the salt-and-pepper noise with densities of 10%

15%

20%

25%

and 30% are added to the test images. The experimental results demonstrate that PSNR obtained by the proposed algorithm combined with the median pre-filtering algorithm is 1.308 dB more than the PSNR value under the traditional median filtering algorithm. Simultaneously

SSIM of the proposed algorithm with the median pre-filtering algorithm is 0.011 higher than that of the traditional median filtering algorithm. For the Poisson noise

PSNR and SSIM of the proposed algorithm approximate those of the AFTV algorithm. However

PSNR and SSIM of the proposed algorithm are 1.59 dB and 0.005

respectively

which are higher than those of the TV algorithm. Experiments were performed on images with three different noise levels. The corresponding PSNR and SSIM values were calculated for comparison. PSNR

SSIM

and image visual effect of the proposed method are superior to those of the TV and AFTV models

particularly for the images polluted by large noise. Meanwhile

the time consumed by the TV model is low but the denoising effect is relatively poor. By contrast

the time consumption for the proposed algorithm is nearly the same as that of the AFTV algorithm. However

the denoising effect is good when the proposed model was used. Moreover

the proposed algorithm performs well in removing a variety of typical noises and can be used universally. In summary

the proposed method is capable of improving the denoising performance caused by the staircase effect for images with severe noise while preserving the weak edge and texture detail more effectively than the TV and AFTV denoising models could.