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 .alpha.. 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.