Noniterative blind image restoration based on estimation of a significant class of point spread functions

Blind image restoration means estimating the true image from an observed degraded image, with incomplete or little prior knowledge of the blur function and the true image. Commonly, iterative or recursive methods are applied to this problem, but they are usually time-consuming, uncertain, and divergent. Focusing on a limited but significant class of point spread functions (heavy-tailed Levy processes), a noniterative blind image restoration method is proposed, which directly estimates the point spread functions from the degraded image's Fourier amplitude and restores the image by general slow evolution of a continuation boundary. This method is based on the fast Fourier transform, so it can accomplish the blind restoration of a 512 X 512 image in seconds of CPU time on a current desktop platform. From several experiments on synthetic blurred images and on actual images, it is found that the quality of the restored images has been greatly improved, and many fine details are restored, by applying this method. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

[1]  J. H. van Hateren,et al.  Modelling the Power Spectra of Natural Images: Statistics and Information , 1996, Vision Research.

[2]  D. Mumford,et al.  Stochastic models for generic images , 2001 .

[3]  Florin Popentiu,et al.  Iterative identification and restoration of images , 1993, Comput. Graph..

[4]  David Mumford,et al.  Statistics of natural images and models , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[5]  D J Field,et al.  Relations between the statistics of natural images and the response properties of cortical cells. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[6]  Deepa Kundur,et al.  A novel blind deconvolution scheme for image restoration using recursive filtering , 1998, IEEE Trans. Signal Process..

[7]  Alfred S. Carasso.  Image restoration and diffusion processes , 1993, Optics & Photonics.

[8]  D. Tolhurst,et al.  Amplitude spectra of natural images. , 1992, Ophthalmic & physiological optics : the journal of the British College of Ophthalmic Opticians.

[9]  Alan V. Oppenheim,et al.  New Technique For Blind Deconvolution , 1981 .

[10]  Alfred S. Carasso,et al.  Direct Blind Deconvolution , 2001, SIAM J. Appl. Math..

[11]  Remco Duits,et al.  On alpha Kernels, Lévy Processes, and Natural Image Statistics , 2005, Scale-Space.

[12]  M A Fiddy,et al.  Blind deconvolution of images by use of neural networks. , 1994, Optics letters.

[13]  D. A. Fish,et al.  Blind deconvolution by means of the Richardson-Lucy algorithm. , 1995 .

[14]  Aggelos K. Katsaggelos,et al.  Iterative identification and restoration of images , 1990, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[15]  Antonio Torralba,et al.  Modeling the Shape of the Scene: A Holistic Representation of the Spatial Envelope , 2001, International Journal of Computer Vision.

[16]  J. C. Dainty,et al.  Iterative blind deconvolution method and its applications , 1988 .

[17]  G. J. Burton,et al.  Color and spatial structure in natural scenes. , 1987, Applied optics.

[18]  Antonio Torralba,et al.  Statistics of natural image categories , 2003, Network.

[19]  Bruce J. West,et al.  Fractional Calculus and the Evolution of Fractal Phenomena , 1999 .

[20]  Deepa Kundur,et al.  Blind Image Deconvolution , 2001 .

[21]  Y. Leroy,et al.  Deconvolution and Weiner filtering of short-range radiometric images , 1993 .

[22]  B. C. McCallum.  Blind deconvolution by simulated annealing , 1990 .

[23]  Tony F. Chan,et al.  Total variation blind deconvolution , 1998, IEEE Trans. Image Process..

[24]  B. R. Hunt,et al.  The Application of Constrained Least Squares Estimation to Image Restoration by Digital Computer , 1973, IEEE Transactions on Computers.

[25]  Luc Van Gool,et al.  An Extended Class of Scale-Invariant and Recursive Scale Space Filters , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  D. Tolhurst,et al.  Amplitude spectra of natural images , 1992 .

[27]  David S. Bright,et al.  APEX method and real-time blind deconvolution of scanning electron microscope imagery , 2001 .