AbstractThe averaged projection filter (APF) is an optimal restoration filter proposed by the present authors in another paper. Here, properties of the APF are discussed in detail. For example, the image component of the restored image with the APF coincides with the original image if the original image belongs to a subspace. For the original images outside the subspace, the image component becomes the oblique projection onto a subspace of the original image in the mean square sense. A noise suppression mechanism of the APF also is clarified by using the null space of the APF. A simpler expression of the APF is given under some assumption. Finally, relations between the APF and the Wiener filter are discussed.