Phase field estimation from single DIC microscopy images using the alternating direction method of multipliers

In this work we discuss total-variation regularized estimation of the phase field from single differential interference contrast microscopy images. The problem is formulated as a convex minimization problem and, resorting to an approximate linear convolution operator, solved by regularized non-circular deconvolution using the alternating directions method of multipliers (ADMM). The solution is derived to allow inversion using a single regularizer. To tackle the problem of ADMM penalty tuning, we further propose the use of a penalty updating strategy that has been shown to be considerably less sensitive to parameter tuning. Results show that, within the limits of the approximate model, the solution is effective, and it can be used to obtain workable estimates of the phase in images of pure-phase biological specimens.