Research On Grouplet Transform Method In Image Processing

This dissertation was supported by the National Natural Science Foundation of China(No.51675258,51075372),National key R & D program(No.2016YFF0203000),the Science and Technology Project of Jiangxi Provincial Education Department(No.GJJ150699)and the Key Laboratory of Digital Signal and Image Processing of Guangdong Province(2014GDDSIPL-01).Based on the Grouplet Transform as the center,a series of new algorithms are proposed for the image reconstruction,image denoising and image fusion.Combining with the new compressive sampling theory,some innovative achievements are obtained.The main contents are summarized as follows:In the first chapter,the necessity of combining Grouplet Transform and Compressice Sensing,the research of this topic is discussed in detail.The development and research progress of Hyper-Wavelets are introduced systematically.In particular,the present situation of Grouplet Transform is briefly summarized.Finally,the main contents and innovations of this paper are listed.In the second chapter,based on the advantages of Grouplet Transform and Compressive Sensing algorithm,an image processing method based on Grouplet-CS is proposed.The method is characterized by the fact that the sparse representation of the Grouplet Transform is fully integrated into the Compressive Sensing,which maximizes the geometric characteristics of the image and eliminates the redundancy and resource waste caused by the traditional Nyquist theory,and can further excavate the image direction,scale and other texture informations,so clearer image quality can be restored even by little sampling points.By reconstruction,it is proved that the method reduces the sparseness and sampling rate of the traditional method and improves the reconstruction quality.In addition,the different reconstruction methods are compared,the studies show that ROMP algorithm overall better than OMP algorithm in the same sparse representation and the same compression ratio.The third chapter mainly focuses on the theory of Compressive Sensing.This paper introduces its main components,analyzes the importance of sparse representation to the whole compressive sensing process,and introduces the general measurement matrix and the basis of selection.Based on the traditional variational Bayesian algorithm,the Grouplet-BCS algorithm is proposed based on the image denoising problem.The Lena simulation study and its use in SAR image denoising are used to prove the unique advantages of the algorithm in image denoising.In the fourth chapter,the characteristics of Wavelet threshold denoising and the defects are discussed in detail.According to the problems existing in Wavelet threshold denoising,adaptive Grouplet threshold denoising is proposed,and its denoising principle and algorithm process are demonstrated in detail.The adaptive Grouplet-CS algorithm and the adaptive Grouplet-BCS algorithm are deduced on the basis,and used together in image denoising to verify the advantages and disadvantages of each method.The applicabilities of various methods are analysed comparatively through the simulation experiment,and its use in SAR images.In the fifth chapter,the Pulse Coupling Neural Network(PCNN)method is introduced.Combined with the advantages of Grouplet Transform in image multi-scale direction and texture mining,a Grouplet-PCNN fusion algorithm is proposed.PCNN can synchronize the transmission pulse,and has the advantage of global coupling,which can obtain the beneficial informations from the complex background.The Grouplet Transform can eliminate the large redundancy of the image and achieve the reconstruction effect better than the Wavelet Transform.The reconstruction precision of this algorithm is proved by the metal fracture image.Chapter sixth summarizes the previous chapters,points out the directions for improvement and further research in the future.