Constrained least-squares image restoration filters for sampled image data

Constrained least-squares image restoration, first proposed by Hunt twenty years ago, is a linear image restoration technique in which the smoothness of the restored image is maximized subject to a constraint on the fidelity of the restored image. The traditional derivation and implementation of the constrained least-squares restoration (CLS) filter is based on an incomplete discrete/discrete (d/d) system model which does not account for the effects of spatial sampling and image reconstruction. For many imaging systems, these effects are significant and should not be ignored. In a 1990 SPIE paper, Park et. al. demonstrated that a derivation of the Wiener filter based on the incomplete d/d model can be extended to a more comprehensive end-to-end, continuous/discrete/continuous (c/d/c) model. In a similar 1992 SPIE paper, Hazra et al. attempted to extend Hunt's d/d modelbased CLS filter derivation to the c/d/c model, but with limited success. In this paper, a successful extension of the CLS restoration filter is presented. The resulting new CLS filter is intuitive, effective and based on a rigorous derivation. The issue of selecting the user-specified inputs for this new CLS filter is discussed in some detail. In addition, we present simulation-based restoration examples for a FLIR (Forward Looking Infra-Red) imaging system to demonstrate the effectiveness of this new CLS restoration filter.