Abstract

In the classical image restoration problem by constrained least-squares, a constraint on the noise variance is combined with a smoothing operation to restore the image and reduce the effect of ill-conditioning. The smoothing operation is not always easy to justify from a physical point of view and therefore has an ad-hoc flavor. We propose an alternative approach to image restoration based on Hilbert space ideas in which the restored image must be at the intersection of sets of vectors that are physically constrained. This approach allows for the incorporation of significant prior knowledge, about both the noise and the signal to be restored. We compare the two approaches analytically and numerically.

© 1991 Optical Society of America