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A new approach to restore images degraded by singular observation processes is proposed. Existing image restoration filters usually assume non-singularity of observation processes. Therefore, we can not obtain desirable result by these filters, especially in case that the degradation processes have high singularity. By the way, it is well known that differential images can be assumed to be Laplacian distributed random vectors. In this paper, we propose a new restoration method for singular observation processes based on this statistical knowledge about images. A numerical example is also presented to verify the efficacy of the proposed method.