Implementation and evaluation of a penalized alternating minimization algorithm for computational DIC microscopy

We present the implementation and evaluation of a penalized alternating minimization (AM) method for the computation of a specimen's complex transmittance function (magnitude and phase) from images captured with Differential Interference Contrast (DIC) microscopy. The magnitude of the transmittance function is constrained to be less than 1. The penalty is on the roughness of the complex transmittance function. Without the penalty, we show via simulation that the difference between the true and estimated transmittance function takes values in the null space of the DIC point-spread function, thereby characterizing the ill-posed nature of this inverse problem. The penalty effectively attenuates larger spatial frequencies that are in this null space. The algorithm is implemented on yeast cell images after proper normalization of the measured data. Preliminary results are promising.