Abstract
A multiple convolution (e.g., an image formed by convolving several individual components) is automatically deconvolvable, provided that its dimension (i.e., the number of variables of which it is a function) is greater than unity. This follows because the Fourier transform of a K-dimensional function (having compact support) is zero on continuous surfaces (here called zero sheets) of dimension (2K − 2) in a space that effectively has 2K dimensions. A number of important practical applications are transfigured by the concept of the zero sheet. Image restoration can be effected without prior knowledge of the point-spread function, i.e., blind deconvolution is possible even when only a single blurred image is given. It is in principle possible to remove some of the additive noise when the form of the point-spread function is known. Fourier phase can be retrieved directly, and, unlike for readily implementable iterative techniques, complex images can be handled as straightforwardly as real images.
© 1987 Optical Society of America
Full Article | PDF ArticleMore Like This
R. H. T. Bates, B. K. Quek, and C. R. Parker
J. Opt. Soc. Am. A 7(3) 468-479 (1990)
P. J. Bones, C. R. Parker, B. L. Satherley, and R. W. Watson
J. Opt. Soc. Am. A 12(9) 1842-1857 (1995)
B. L. Satherley and P. J. Bones
Appl. Opt. 33(11) 2197-2205 (1994)