Research On Image Restoration Based On Wavelet Transform

Data is becoming increasingly significant in many industries in the big data era,which raises the bar for data integrity.Images carry a lot of information since they are a special type of data.Unfortunately,images may become tainted by noise or lose some information during the collecting and transmission process,so the image restoration problem has been an important research content in the field of image processing.The image has sparse structure under the wavelet multiscale transform since it is a high-dimensional signal.As a more recent outcome of wavelet theory,the directional wavelet multiscale system is capable of efficiently obtaining directional characteristics in images.In order to study the image restoration problem,we integrate the directional wavelet multiscale system and total variation in this thesis.The research presented in this thesis,which is primarily concerned with the problem of rain removal from single image,covers the two parts listed following:1.An image rain streaks removal method based on shearlet transform and unidirec-tional total variation is given for the single-image rain removal problem,with the goal of removing vertical or almost vertical rain streaks in images with rain.First,the intrinsic prior knowledge of the background layer and rain streaks is fully exploited.The sparsity of the shearlet transform decomposition coefficients of the background layer in the vertical direction is exploited to retain the background layer information,and the unidirectional to-tal variation is used to constrain the smoothness of the rain streaks in the vertical direction.A convex optimization model for single-image rain streaks removal is developed.The al-ternating direction method of multipliers is then used to design model solving algorithm.Numerical experimental results show that the provided method can effectively remove rain streaks and preserve the details of the background layer,illustrating the superiority of the method.2.For the single-image directional rain removal problem,image rain streaks removal methods combining shearlet transform and directional total variation are provided.Based on the directional characteristics of rain streaks,the information of the background layer is constrained using the shearlet transform or non-subsampled shearlet transform in the di-rection of rain streaks,and the directional smoothness of the rain streaks is characterized by the directional total variation in the rain direction.The7)_2,1norm is employed to inscribe the sparsity of rain streaks.We provide two deraining models:one based on shearlet trans-form and directional total variation,the other on non-subsampled shearlet transform and directional total variation.By utilizing the split augmented Lagrangian shrinkage algo-rithm,the solution algorithms are designed for the two models respectively.According to numerical experimental results on synthetic and real data,the two methods given can ef-fectively remove directional rain streaks while retaining as much of the edge information and high frequency information of the background layer.The experimental results also show that the method based on the non-subsampled shearlet transform typically performs better than the shearlet transform-based method.