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Constrained Restoration and the Recovery of Discontinuities
March 1992 (vol. 14 no. 3)
pp. 367-383

The linear image restoration problem is to recover an original brightness distribution X/sup 0/ given the blurred and noisy observations Y=KX/sup 0/+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/ 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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Index Terms:
image deburring; discontinuity recovery; picture processing; concave stabiliser; linear image restoration; brightness distribution; point spread function; ill-conditioned inverse problems; low-level computer vision; cost functional; computer vision; inverse problems; picture processing
D. Geman, G. Reynolds, "Constrained Restoration and the Recovery of Discontinuities," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 3, pp. 367-383, March 1992, doi:10.1109/34.120331
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