Research On Adaptive Image Denoising Based On Partial Differential Equations And Wave Domain

Noise can be understood as a basic signal distortion,which can hinder the observation and analysis of images,so any progress in the field of image denoising can help to strengthen our understanding of basic image statistics and processing.This paper first proposes a denoising method combining dual-tree complex wavelet and Canny algorithm,establishes a denoising model based on fractional differential algorithm,and proposes a spatially adaptive multi-order total variation denoising method based on wavelet threshold function,and verify the results through simulation experiments,and finally draw conclusions.The main research contents are as follows:1.For traditional wavelet processing,it has poor directional sensitivity,invariance of displacement and large redundancy.An image denoising method combining dual-tree complex wavelet and Canny algorithm is proposed.First,wavelet shrinkage is used to set the wavelet coefficients of all proportions and subbands as thresholds.Then,the edge detection characteristics of Canny algorithm are used to design a control function to perform edge detection and finally inverse dual-tree complex wavelet transform processing can not only effectively remove image noise,but also protect the edge texture information of the image.The denoising performance is also more ideal,with certain advancedness and practicality.2.For the traditional denoising scheme,it may produce unexpected image blurring effect,which will affect the image edge and other details.Therefore,an adaptive image denoising model based on fractional differential algorithm is proposed.First,the image gradient is used for edge detection,and then the properties of the Gaussian curvature and the fractional differential algorithm are combined to establish a fractional differential algorithm from the local variance of the image.The new model effectively controls the image edge texture detail information.The internal information structure protection is more complete,and the denoising performance is more ideal,which has certain advancedness and practicability.3.Aiming at the shortcomings of traditional first-order and second-order total variation denoising models in the image processing process,a novel spatially adaptive multi-order variational regularization function is proposed.Regularization-based formulas for adjusting these weights are combined.First,filter the wavelet threshold,then the denoising image isdecomposed by wavelet,and then the Canny algorithm is used to detect the edges to avoid losing the edge texture information.Meanwhile it is combined with the spatial adaptive multi-order total variation denoising model for processing.The results show that the proposed method can better deal with noise and retain image information.