Sparse array imaging using low-rank matrix recovery

Co-array based processing enables sparse arrays to achieve the resolution of uniform arrays in array imaging applications. In particular, a desired point spread function may be synthesized by coherently adding together several component images obtained using different complex-valued physical element weights. However, ambiguities in the weight assignment arise when the co-array of a given array configuration contains redundancies. A suboptimal assignment leads to using more component images that necessary, which may increase the acquisition time of the final image. This paper shows that the number of component images in active transmit-receive imaging can be minimized by formulating a low-rank matrix recovery problem that is solved uniquely and efficiently using convex optimization. The suggested method may also be applied to passive sensing with minor modifications. The performance of the proposed method is compared to uniformly distributing co-array weights among physical array elements, which is typically used for simplicity. Numerical simulations show that the suggested method uses up to 60% fewer component images than uniform assignment.