Efficient reformulation of image reconstruction with compressive sensing

Sparse reconstruction techniques are used with radar imaging to construct high resolution images from a minimal amount of data. This reconstruction is computationally expensive. This paper proposes a computationally efficient formulation of radar imaging with and without compressive sensing. The dictionary matrix is decomposed into a product of a Toeplitz and sparse matrices to perform the required multiplication in an efficient way. The measurement matrix is rearranged to preserve the structure. The reduction in the order of complexity at differed compression rates as a result of the proposed formulation is evaluated.