ISSN:
1531-5878
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract We study the following type of filtering problem: consider an image on ℤ2, that is, a nonnegative function on the vertices of a grid, which represents the brightness at each of these points. We assume that there is, however, a “smudging” effect. That is, what ought to be a point of light becomes the point together with a halo about it, visualized by a distribution of light which is greatest at the point itself and decreases with the distance. So what we actually see is a blurry image. In this article we investigate methods for clearing up the image, i.e. reconstructing the original function from the blurry haloed image when the halo decays exponentially, and also for some haloes with small finite support. This task is usually performed by inverting the convolution operator induced by the halo (that is, by Fourier analysis). We introduce a different recovery procedure, based upon a family of filtering operators that change from point to point. For the finitely supported haloes, this procedure compares favorably with the Fourier methods. Moreover, in principle it is more general, because it does not require assumptions of invariance under translation. In full generality, however, we are able to recover images not on grids, but only on trees.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01183779
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