We propose a methodology that exploits large and diverse data sets to accurately estimate the ambient medium's Green's functions in strongly scattering media. Given these estimates, obtained with and without the use of neural networks, excellent imaging results are achieved, with a resolution that is better than that of a homogeneous medium. This phenomenon, also known as super-resolution, occurs because the ambient scattering medium effectively enhances the physical imaging aperture. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

We propose an approach for imaging in scattering media when large and diverse data sets 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 Multi-Dimensional Scaling 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 the connectivity needed in the second step. Through simulation experiments, we show that the proposed approach is able to provide images in complex media whose resolution is that of a homogeneous medium.

The Noise Collector for sparse recovery in high dimensions Miguel Moscoso, Alexei Novikov †, George Papanicolaou ‡, Chrysoula Tsogka § August 14, 2019 Abstract The ability to detect sparse signals from noisy high-dimensional data is a top priority in modern science and engineering. A sparse solution of the linear system A ρ b 0 can be found efficiently with an null 1-norm minimization approach if the data is noiseless. Detection of the signal's support from data corrupted by noise is still a challenging problem, especially if the level of noise must be estimated. We propose a new efficient approach that does not require any parameter estimation. We introduce the Noise Collector (NC) matrix C and solve an augmented system A ρ C η b 0 e, where e is the noise. We show that the l 1-norm minimal solution of the augmented system has zero false discovery rate for any level of noise and with probability that tends to one as the dimension of b 0 increases to infinity. We also obtain exact support recovery if the noise is not too large, and develop a Fast Noise Collector Algorithm which makes the computational cost of solving the augmented system comparable to that of the original one. Finally, we demonstrate the effectiveness of the method in applications to passive array imaging. In the noiseless case, ρ can be found exactly by solving the optimization problem [9] ρ arg min ρ null ρnull null 1, subject to A ρ b, (2) provided the measurement matrix A R N K satisfies additional conditions, e.g., decoherence or restricted isometry properties [11, 4], and the solution vector ρ has a small number M of nonzero components or degrees of freedom.