A New Technique for Constrained Image Restoration by Compensating the PSF

Abstract

The idea behind the method of constrained image restoration by compensating the point spread function (PSF) is to obtain a restoration filter such that when it is convolved with the PSF the resulting function, called the composite point spread function (CPSF), satisfies appropriate optimization criteria. Ideally it would be desirable to obtain a CPSF that is a delta function; i.e., the restoration filter would be the inverse filter. However this is not possible due to the instability and serious noise amplification of such filters. Stable filters using this approach can be obtained by minimizing an appropriate width measure while constraining the output noise power [1-3]. There are significant advantages in using this method for image (or signal) restoration over other commonly employed procedures. First, the restoration operator can be constrained to a specific size, thereby controlling the duration of transients due to edge effects and reducing the computational burden. Second, the procedure is not dependent on statistics of the image but only on the sensor PSF, the noise, and the sampling grid. Third, for image enhancement it is possible to combine the interpolation and deconvolution procedures into a single operation, thereby increasing the speed and efficiency of the processing.