Truncated Fractional-Order Total Variation Model for Image Restoration

Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed.In the existing works,the Grunwald–Letnikov fractional-order derivative is usually used,where the Dirichlet homogeneous boundary condition can only be considered and therefore the full lower triangular Toeplitz matrix is generated as the discrete partial fractional-order derivative operator.In this paper,a modified truncation is considered in generating the discrete fractional-order partial derivative operator and a truncated fractional-order total variation(tFoTV)model is proposed for image restoration.Hopefully,first any boundary condition can be used in the numerical experiments.Second,the accuracy of the reconstructed images by the tFoTV model can be improved.The alternating directional method of multiplier is applied to solve the tFoTV model.Its convergence is also analyzed briefly.In the numerical experiments,we apply the tFoTV model to recover images that are corrupted by blur and noise.The numerical results show that the tFoTV model provides better reconstruction in peak signal-to-noise ratio(PSNR)than the full fractional-order variation and total variation models.From the numerical results,we can also see that the tFoTV model is comparable with the total generalized variation(TGV)model in accuracy.In addition,we can roughly fix a fractional order according to the structure of the image,and therefore,there is only one parameter left to determine in the tFoTV model,while there are always two parameters to be fixed in TGV model.

Noise Reduction of Welding Defect Image Based on NSCT and Anisotropic Diffusion

In order to reduce noise effectively in the welding defect image and preserve the minutiae information, a noise reduction method of welding defect image based on nonsubsampled contourlet transform(NSCT) and anisotropic diffusion is proposed. Firstly, an X-ray welding defect image is decomposed by NSCT. Then total variation(TV) model and Catte_PM model are used for the obtained low-pass component and band-pass components, respectively. Finally, the denoised image is synthesized by inverse NSCT. Experimental results show that, compared with the hybrid method of wavelet threshold shrinkage with TV diffusion, the method combining NSCT with P_Laplace diffusion, and the method combining contourlet with TV model and adaptive contrast diffusion, the proposed method has a great improvement in the aspects of subjective visual effect, peak signal-to-noise ratio(PSNR) and mean-square error(MSE). Noise is suppressed more effectively and the minutiae information is preserved better in the image.