  Adaptive optics (AO) corrected ood imaging of the retina is a popular
technique for studying the retinal structure and function in the living eye.
However, the raw retinal images are usually of poor contrast and the
interpretation of such images requires image deconvolution. Different from
standard deconvolution problems where the point spread function (PSF) is
completely known, the PSF in these retinal imaging problems is only partially
known which leads to the more complicated myopic (mildly blind) deconvolution
problem. In this paper, we propose an efficient numerical scheme for solving
this myopic deconvolution problem with total variational (TV) regularization.
First, we apply the alternating direction method of multipliers (ADMM) to
tackle the TV regularizer. Specifically, we reformulate the TV problem as an
equivalent equality constrained problem where the objective function is
separable, and then minimize the augmented Lagrangian function by alternating
between two (separated) blocks of unknowns to obtain the solution. Due to the
structure of the retinal images, the subproblems with respect to the fidelity
term appearing within each ADMM iteration are tightly coupled and a variation
of the Linearize And Project (LAP) method is designed to solve these
subproblems efficiently. The proposed method is called the ADMM-LAP method.
Theoretically, we establish the subsequence convergence of the ADMM-LAP method
to a stationary point. Both the theoretical complexity analysis and numerical
results are provided to demonstrate the efficiency of the ADMM-LAP method.
