Compressive Sensing in the Tactical Underwater Environment - MP 45-09 - (MP 34-10)

The theory of compressive sensing (CS) will be extended to the design of arrays for underwater systems. The underlying theory is applicable to arbitrary sensor arrays, but the focus will be placed on synthetic aperture sonar (SAS). The proposed research will integrate CS with the closely related and evolving field of matrix completion. Concerning the latter, it is assumed that a matrix of noisy data are available, but the matrix is only partially filled; the objective is to infer the missing matrix elements. The connection between the latter and CS is that CS is based upon the assumption that the data is compressible in a basis, implying a low information dimensionality. Similarly, in matrix completion it is assumed that the matrix is of low rank (another representation of low inherent information dimensionality). In the proposed research we will investigate these emerging fields in the context of sparsely sampling the data along a SAS aperture, as well as for physical apertures with uniform or random inter-element spacing. We will also work closely with Navy laboratories to apply the theory to existing systems.