2019/02/28 by Manu Ghulyani, Ghulyani, Manu, Muthuvel Arigovindan +1
Engineering · Medicine · #FOS: Electrical engineering #Image and Video Processing (eess.IV) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques #Ultrasound Imaging and Elastography #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1902.11173
openalex publication_date 2019/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Image acquisition in many biomedical imaging modalities is corrupted by\nPoisson noise followed by additive Gaussian noise. While total variation and\nrelated regularization methods for solving biomedical inverse problems are\nknown to yield high quality reconstructions, such methods mostly use\nlog-likelihood of either Gaussian or Poisson noise models, and rarely use mixed\nPoisson-Gaussian (PG) noise model. There is a recent work which deals with\nexact PG likelihood and totalariation regularization. This method is developed\nusing the log-likelihood of PG model along with total variation regularization\nadapts the primal-dual splitting algorithm, whose step size is restricted to be\nbounded by the inverse of the Lipschitz constant of PG log-likelihood. This\nleads to limitations in the convergence speed. On the other hand, ADMM methods\ndo not have such step size restrictions; however, ADDM has never been applied\nfor this problem, for the possible reason that PG log-likelihood is quite\ncomplex. In this paper, we develop an ADMM based optimization for total\nvariation minimizing image restoration under PG log-likelihood. We achieve this\nby first developing a novel iterative method for computing the proximal\nsolution of PG log-likelihood, deriving the termination conditions for this\niterative method, and then integrating into a provable convergent ADMM scheme.\nThe effectiveness of the proposed methods is demonstrated using restoration\nexamples.\n