Correlation-informed ordered dictionary learning for imaging in complex media

We propose a method for imaging in scattering media when large and diverse datasets are available. It has two steps. Using a dictionary learning algorithm the first step estimates the true Green's function vectors as columns in an unordered sensing matrix. The array data comes from many sparse sets of sources whose location and strength are not known to us. In the second step, the columns of the estimated sensing matrix are ordered for imaging using the multidimensional scaling algorithm with connectivity information derived from cross-correlations of its columns, as in time reversal. For these two steps to work together, we need data from large arrays of receivers so the columns of the sensing matrix are incoherent for the first step, as well as from sub-arrays so that they are coherent enough to obtain connectivity needed in the second step. Through simulation experiments, we show that the proposed method is able to provide images in complex media whose resolution is that of a homogeneous medium.