SPACE-VARYING RESTORATION OF OPTICAL-IMAGES

The improvement in optical image quality is now generally attempted in two stages. The first stage involves techniques in adaptive optics an d occurs as the observed image is initially formed. The second stage o f enhancing the quality of optical images generally occurs off line an d consists of the postprocessing step of image restoration. Image rest oration is an ill-posed inverse problem that involves the removal or t he minimization of degradations caused by noise and blur in an image, resulting from, in this case, imaging through a medium, Our work conce rns a new space-varying regularization approach and associated techniq ues for accelerating the convergence of iterative image postprocessing computations. Denoising methods, including total variation minimizati on, followed by segmentation-based preconditioning methods for minimum residual conjugate gradient iterations, are investigated. Regularizat ion is accomplished by segmenting the image into (smooth) segments and varying the preconditioners across the segments. The method appears t o work especially well on images that are piecewise smooth. Our algori thm has computational complexity of only O(ln(2) log n), where n(2) is the number of pixels in the image and l is the number of segments use d. Also, parallelization is straight-forward. Numerical tests are repo rted on both simulated and actual atmospheric imaging problems. Compar isons are made viith the case where segmentation is not used. It is fo und that our approach is especially attractive for restoring images wi th low signal-to-noise ratios, and that magnification of noise is effe ctively suppressed in the iterations, leading to a numerically efficie nt and robust regularized iterative restoration algorithm. (C) 1997 Op tical Society of America.