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Adaptive optics (AO) corrected ood imaging of the retina is a populartechnique for studying the retinal structure and function in the living eye.However, the raw retinal images are usually of poor contrast and theinterpretation of such images requires image deconvolution. Different fromstandard deconvolution problems where the point spread function (PSF) iscompletely known, the PSF in these retinal imaging problems is only partiallyknown which leads to the more complicated myopic (mildly blind) deconvolutionproblem. In this paper, we propose an efficient numerical scheme for solvingthis myopic deconvolution problem with total variational (TV) regularization.First, we apply the alternating direction method of multipliers (ADMM) totackle the TV regularizer. Specifically, we reformulate the TV problem as anequivalent equality constrained problem where the objective function isseparable, and then minimize the augmented Lagrangian function by alternatingbetween two (separated) blocks of unknowns to obtain the solution. Due to thestructure of the retinal images, the subproblems with respect to the fidelityterm appearing within each ADMM iteration are tightly coupled and a variationof the Linearize And Project (LAP) method is designed to solve thesesubproblems efficiently. The proposed method is called the ADMM-LAP method.Theoretically, we establish the subsequence convergence of the ADMM-LAP methodto a stationary point. Both the theoretical complexity analysis and numericalresults are provided to demonstrate the efficiency of the ADMM-LAP method.

An ADMM-LAP method for total variation myopic deconvolution of adaptive optics retinal images