Image Denoising Model Based On Fractional-order Partial Differential Equation And Split Bregman Algorithm

The initial stage of image processing is image denoising,which is a key link in subsequent operations such as image restoration and image enhancement,and plays a key role in image processing.Based on the theoretical knowledge of integer order calculus,researchers at home and abroad have given various integer order partial differential equation denoising models,such as TV model,P-M model,etc.Although these models have a certain denoising effect,but However,it is easy to produce "staircase effect" and cannot preserve the texture details of the image well.Fractional calculus equations are essentially a generalization of integer calculus equations.Fractional calculus operators not only have memory,but also have non-locality and weak derivative properties,and play an important role in the field of image processing.In the field of image denoising,a fractional calculus operator of appropriate order can not only greatly preserve edge and texture details,but also non-linearly preserve the texture information of the smooth area of the image,so as to achieve better image denoising effect.In this paper,the fractional differential operator is introduced into the TV model,and at the same time,the fractional gradient is used to improve the fidelity term of the model,and the FTV model is obtained.The fractional gradient fidelity term can achieve smooth images and overcome the "step effect",and then applied the Split Bregman algorithm to the solution of the FTV model,gave the iterative form of the FTV model in the numerical experiment,and proved that the Split Bregman algorithm can be applied to the model through experiments.Then,the superiority of the FTV model proposed in this paper is verified by comparing the denoising effect of the improved FTV model in this paper with other integer-order models and fractional-order models.The results obtained by numerical experiments show that the improved FTV model achieves the expected results,indicating that the FTV model proposed in this paper has better image denoising effect.