A novel blind deconvolution is proposed to seek for basis patterns and their location maps inside a nonnegative data matrix. Basis patterns can have different sizes, and shift in independent directions. Moreover, the location maps can be low-rank or rank-one matrices composed by two relatively small and tall matrices or by two vectors. A general framework to solve this problem together with algorithms are introduced. The experiments on music and texture decomposition will confirm performance of our method, and of the proposed algorithms.