Quasi-Newton approach to nonnegative image restorations

Image restoration, or deblurring, is the process of attempting to correct f or degradation in a recorded image. Typically the blurring system is assume d to be linear and spatially invariant, and fast Fourier transform (FFT) ba sed schemes result in efficient computational image restoration methods. Ho wever, real images have properties that cannot always be handled by linear methods. In particular, an image consists of positive light intensities, an d thus a nonneg ativity constraint should be enforced. This constraint and other ways of incorporating a priori information have been suggested in var ious applications, and can lead to substantial improvements in the reconstr uctions. Nevertheless, such constraints are rarely implemented because they lead to nonlinear problems which require demanding computations. We sugges t efficient implementations for three nonnegatively constrained restoration s schemes: constrained least squares, maximum likelihood and maximum entrop y. We show that with a certain parameterization, and using a Quasi-Newton s cheme, these methods are very similar. In addition, our formulation reveals a connection between our approach for maximum likelihood and the expectati on;maximization (EM) method used extensively by astronomers. Numerical expe riments illustrate that our approach is superior to EM both in terms of acc uracy and efficiency. (C) 2000 Elsevier Science Inc. All rights reserved.