We apply the filter bank method, which extracts from a strongly defocused image the information on the amount of defocus, i.e., the information on the object distance, and simultaneously restores the object, to a defocused image of extremely low intensity, which is detectable only with a photon counting camera. Experimental results show that the information of the defocus amount can be extracted from such a blurred photon image, and the original object itself is simultaneously restored. The influence of the photon noise on the distance estimation is also quantitatively investigated. Then, the maximum likelihood-expectation maximization (ML-EM) method is adopted for image restoration, and the results are compared with those obtained by applying the conventional Wiener filter. It is experimentally shown that the ML-EM produces better image restoration than the Wiener filter in the extremely low intensity region where the maximal number of photons per pixel does not exceed about 450.