caa a22 4500 477097367 CHVBK 20180405111531.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF01183779 doi (NATIONALLICENCE)springer-10.1007/BF01183779 Image recovery from exponential blurring [Elektronische Daten] [Joel Cohen, Flavia Colonna, Massimo Picardello] 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. Birkhäuser, 1996 Cohen Joel Department of Mathematics, University of Maryland, 20742, College Park, MD aut Colonna Flavia Department of Mathematical Sciences, George Mason University, 4400 University Drive, 22030, Fairfax, VA aut Picardello Massimo Dipartimento di Matematica, Università di Roma "Tor Vergata,”, Via della Ricerca Scientifica, 00133, Roma, Italy aut Circuits, Systems and Signal Processing Birkhäuser-Verlag 15/2(1996-03-01), 261-274 0278-081X 15:2<261 1996 15 34 https://doi.org/10.1007/BF01183779 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01183779 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cohen Joel Department of Mathematics, University of Maryland, 20742, College Park, MD aut NATIONALLICENCE 700 1- Colonna Flavia Department of Mathematical Sciences, George Mason University, 4400 University Drive, 22030, Fairfax, VA aut NATIONALLICENCE 700 1- Picardello Massimo Dipartimento di Matematica, Università di Roma "Tor Vergata,”, Via della Ricerca Scientifica, 00133, Roma, Italy aut NATIONALLICENCE 773 0- Circuits, Systems and Signal Processing Birkhäuser-Verlag 15/2(1996-03-01), 261-274 0278-081X 15:2<261 1996 15 34 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer