Fractional-order iterative regularization method for total variation based image denoising

摘要

The iterative regularization method proposed by Osher et al. for total variation based image denoising can preserve textures well and has received considerable attention in the signal and image processing community in recent years. However, the iteration sequence generated by this method converges monotonically to the noisy image, and therefore this iteration must be terminated opportunely with an "optimal" stopping index, which is difficult in practice. To overcome this shortcoming, we propose a novel fractional-order iterative regularization model by introducing the fractional-order derivative. The new model can be considered as an interpolation between the traditional total variation model and the traditional iterative regularization model. Numerical results demonstrate that with a fitting order of derivative, the denoised image sequence generated by this model can converge to a denoised image with high peak signal to noise ratio and high structural similarity index after a few iteration steps, and therefore we can terminate the iteration according to some most used termination conditions. Moreover, we propose an experience method to choose the order of derivative adaptively for the partly textured images to improve the performance of noise removal and texture preservation. The adaptive method has low computational cost and can improve the result visually efficiently.