Image restoration by a powerful maximum entropy method

Abstract A powerful iterative algorithm has been developed which produces a maximum entropy solution to the image restoration problem. It has been applied to images containing up to 1024 × 1024 pixels and has been implemented on both mini and mainframe computers. Unlike some methods, the algorithm does not require the point-spread function to have any special symmetry properties. Examples are given of the application of this method both to artificially and to experimentally blurred photographs, and also to an X-ray radiograph, blurred by the size of the radiation source. For comparison, restorations of some of these images by the linear method of constrained least squares are also shown. The maximum entropy algorithm revealed detail on the images not seen in the linear restorations, but which are known to exist. Maximum entropy is also applied to the reconstruction of images from sparse data, which no comparable linear algorithm can handle.

[1]  B. Frieden.  Restoring with maximum likelihood and maximum entropy. , 1972, Journal of the Optical Society of America.

[2]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[3]  Stephen J. Wernecke,et al.  Maximum Entropy Image Reconstruction , 1977, IEEE Transactions on Computers.

[4]  S. J. Wernecke.  Two‐dimensional maximum entropy reconstruction of radio brightness , 1977 .

[5]  B. Frieden.  Statistical models for the image restoration problem , 1980 .

[6]  D. Gennery.  Determination of optical transfer function by inspection of frequency-domain plot , 1973 .

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

[8]  R. B. Lazarus,et al.  Maximum entropy restoration of laser fusion target x-ray photographs , 1976 .

[9]  J. Skilling,et al.  Deconvolution by maximum entropy, as illustrated by application to the jet of M87 , 1980 .

[10]  W Swindell,et al.  Restored Pictures of Ganymede, Moon of Jupiter , 1976, Science.

[11]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[12]  Elijah Polak,et al.  Computational methods in optimization , 1971 .

[13]  G. N. Minerbo,et al.  MENT: A maximum entropy algorithm for reconstructing a source from projection data , 1979 .

[14]  S. Gull,et al.  Maximum entropy algorithm applied to image enhancement , 1980 .

[15]  S. Gull,et al.  Image reconstruction from incomplete and noisy data , 1978, Nature.

[16]  E. F. Haugh.  A Structural Theory for the Selwyn Granularity Coefficient , 1963 .

[17]  Claude E. Shannon,et al.  The mathematical theory of communication , 1950 .

[18]  J. F Boulter.  Interactive digital image restoration and enhancement , 1979 .