Abstract: The present invention provides a method for image deblurring based on correctly specifying the lack of smoothness in the unknown desired sharp image, in terms of Lipschitz (Besov) space classification. The method makes essential use of Singular Integrals and Fast Fourier Transform (FFT) algorithms to estimate the image's Lipschitz exponent ?. Such Singular Integrals and Fast Fourier Transforms are then used in a method for regularizing the ill-posed deblurring problem, resulting in a fast, direct, (i.e., non-iterative) computationally effective deblurring procedure.

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 as .rho.(.xi.,.eta.)=exp{-.SIGMA..sup.j.sub.i=1 .lambda..sub.i (.xi..sup.2 +.eta..sup.2).sup..beta.i }.lambda.i.gtoreq.0, 0<.beta.i<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.

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.