Image Deblurring In The Presence Of Poisson Noise

Image restoration is an important research topic in the field of image processing.Its main objective is to recover clear images from degraded/noisy images.This thesis mainly studies the restoration of blurred images in the presence of Poisson noise.First,the Poisson noise model is transformed according to the Bayesian principle and the maximum posterior probability,and then the signal is sparsely represented using the sparse characteristics of the sparse domain,and the optimal model is established and solved for the problem.Finally,an effective restoration of blurred images under Poisson noise is achieved.The main research work in this thesis includes:1.Based on the known prior information of the blur,the restoration of the blurred image under Poisson noise is studied,and two restoration models constructed by different sparse representations are proposed.In order to make the full use of the sparse representation to effectively recover the image,group sparse adaptive dictionary is used to sparsely represent the image,and1-norm as a regularization term is used to establish an optimization model.To solve the optimization problem,the alternating direction method of multipliers(ADMM)optimization algorithm is introduced to obtain the sparse solution of the optimization model.In addition,in order to reduce the complexity of the adaptive dictionary operation,the tight wavelet frame is also explored to sparsely represent the image.The experimental results show that the proposed algorithms can effectively recover blurred images in the presence of Poisson noise.2.The blind restoration of the blurred image in the presence of Poisson noise is studied now.The main challenge is to simultaneously estimate the underlying latent image and blur kernel because the blur kernel is unknown.In order to solve this problem,the image and blur kernel are respectively sparsely represented using the group sparse adaptive dictionary or the tight wavelet frame system,and then 1-norm is utilized to construct a joint optimization model.Based on that,two joint optimization models using different sparse domains are developed.To effectively solve the joint optimization problem,a two-step iterative solution strategy is proposed,which decomposes the joint optimization problem into two sub-problems: denoising and deblurring,and then alternates the problems until convergence.For each sub-problem,ADMM algorithm is still used to obtain the corresponding solutions.The results demonstrate the superior performance of the proposed method over the competing approaches,and from the restorations of the real images,the proposed method also shows its capacity to recover images in the practical applications.