This paper shows that blind deconvolution has only finite solutions when an original image and a point spread function are nonzero over a restricted domain, in other words, an observed image has a compact support. The key of the proof is to use z-transformations and factorizations of polynomials. Then, we propose an algorithm to find all finite solutions under the boundary condition. Finally, we confirm that we can extract all sets of an original image and a point spread function from a degraded image by using our algorithm in numerical examples.