Constrained restoration and the recovery of discontinuities
Geman, D.
Reynolds, G.
Dept. of Math. & Stat., Massachusetts Univ., Amherst, MA;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Mar 1992
Volume: 14,
Issue: 3
On page(s): 367-383
ISSN: 0162-8828
References Cited: 30
CODEN: ITPIDJ
INSPEC Accession Number: 4151468
Digital Object Identifier: 10.1109/34.120331
Current Version Published: 2002-08-06
Abstract
The linear image restoration problem is to recover an original
brightness distribution X0 given the blurred and noisy
observations Y=KX0+B, where K and B represent the point
spread function and measurement error, respectively. This problem is
typical of ill-conditioned inverse problems that frequently arise in
low-level computer vision. A conventional method to stabilize the
problem is to introduce a priori constraints on X0 and design
a cost functional H(X) over images X, which is a weighted average of the
prior constraints (regularization term) and posterior constraints (data
term); the reconstruction is then the image X, which minimizes H. A
prominent weakness in this approach, especially with quadratic-type
stabilizers, is the difficulty in recovering discontinuities. The
authors therefore examine prior smoothness constraints of a different
form, which permit the recovery of discontinuities without introducing
auxiliary variables for marking the location of jumps and suspending the
constraints in their vicinity. In this sense, discontinuities are
addressed implicitly rather than explicitly
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