Constrained restoration and the recovery of discontinuities
IEEE Trans Pattern Anal Mach Intell, 14 (3):
367-383 (1992)DOI: 10.1109/34.120331
Abstract
The linear image restoration problem is to recover an original brightness
distribution X<sup>0</sup> given the blurred and noisy observations
Y=KX<sup>0</sup>+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 X<sup>0</sup> and designa 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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