Skellam Distribution Based Methods For Photon-limited Poisson Noisy Image Reconstruction

Photon counting imaging technology is widely used in night vision imaging,as-trosurveillance and X-ray astronomy and medical imaging system.The imaging devices only receive limited number of photons because of hardware equipment and the imaging conditions.The shot noise of Poisson distribution in the photon counting imaging pro-cess can seriously reduce the imaging quality and generate low quality photon-limited Poisson images.However,information loss and structural damage in photon-limited Poisson noisy image lead to great difficulties for accurate computation of the non-local similarities and detection of local geometric structure of images.So many meth-ods of Poisson image reconstruction in high photon conditions are better,and they are no longer effective for low photon Poisson images.In recent years,reconstruction of photon-limited Poisson image is urgent demand and particularly challenging in many application fields such as security monitoring,astronomy and medical imaging.For the photon-limited Poisson image denoising,this paper focus on the Skellam distribution which is the difference between two independent Poisson random variables.We make full use of photon-limited statistical correlation between pixels to improve the quality of Poisson image reconstruction.The research has important theoretical significance and extensive application value.The main research content,and innovation are as follows:(1)Skellam distribution based adaptive two-stage non-local methods for photon-.limited Poisson noisy image reconstructionAs we all know,accurate computation of similarities between non-local patches is crucial for any non-local method.However,information loss and structural damage in photon-limited Poisson noisy image lead to great difficulties for accurate compu-tation of the non-local similarities.To remedy this,we propose a new method to pro-vide a pre-reconstructed image.The computation of the similarities between non-local patches is guided and affected by the obtained prereconstructed image.The method improves the performance of photon-limited Poisson noisy image reconstruction.In this paper,we aim to provide a better prereconstructed image which base on Skel-lam distribution.Firstly,we propose an improved adaptive homogenous patches detec-'tion method.And fitting Skellam-Intensity relationship between the pixels intensity and skellam parameters based on the homogeneous patches detection.Secondly,we estimate every skellam parameter by the Skellam-Intensity relationship and acceptance range of intensity difference.Moreover,we obtain a pre-reconstructed image based on skellam pa-rameters and acceptance range of intensity difference.Lastly,we propose the improved non-local method which the computation of the similarities between non-local patches is guided by the obtained prereconstructed image.Numerical experiments show that our method can provide a better pre-reconstructed image,and therefore can improve the performance of the PNLM method and reduce the computational cost of the NLPCA method efficiently.(2)Poisson-Skellam distribution based conditional random field com-bined Plug-and-Play scheme for photon-limited poisson image denoisingFor photon-limited Poisson images,many prior image modeling methods based on geometric structure detection are no longer valid because of the severe destruction of geometric structure.So the statistical relationship between pixels statistical prior modeling is very important.But most of photon-limited Poisson image reconstruction methods only take into account the Poisson distribution between the observed images and clean images.In this paper,we assume that there is a Markov between the pixels in the real image,and a conditional random field model is established.This framework integrates the correlation between the latent clean image and the observed image which is measured by an external interaction potential function and the statistical correlation of the local pixels in the clean image which is measured by a inner interaction potential function.We define the inner interaction potential function and the external interac-tion potential function according the Skellam distribution and the Poisson distribu-tion,respecti,vely.And introduce a spatial weighting function.Moreover,introducing regularization term into the CRF model,we proposed our regularized Poisson-Skellam distribution based CRF model for photon-limited Poisson noise removal.Similar to the P4IP method,we propose an alternating iterative algorithm under the plug-and-play framework to solve the new model efficiently.Our method uses more internal statistical prior with real images by introducing the interaction potential function based on the Skellam distribution.Numerical experiments show that the method can effectively im-prove the reconstruction image peak signal-to-noise ratio and the reconstruction image quality.