Abstract: The image restoration system and method of the present invention is applied to point spread functions p(x,y) which may be described in the Fourier domain asp(.xi.,.eta.)=exp{-.SIGMA..sub.i=1.sup.J .lambda..sub.i (.xi..sup.2 +.eta..sup.2).sup..beta..sbsp.i }, .lambda..sub.i .gtoreq.0, 0<.beta..sub.i .ltoreq.1, to improve noise performance and permit identification of fine detail. The novel method formulates the image restoration problem as a problem in the partial differential equations describing diffusion phenomena using a new type of a priori constraint. The restored image is obtained by minimizing a quadratic functional incorporating this new constraint. The solution of the minimization problem may be obtained directly by means of fast Fourier transform algorithms. The restoration method may be performed as a sequence of partial restorations as t.dwnarw.0 wherein the partial restorations become sharper and noisier as t.dwnarw.0, or as a single full restoration.