Cramer-Rao lower bounds for support-constrained and pixel-based multiframe blind deconvolution

Abstract

Multi-frame blind deconvolution (MFBD) algorithms can be used to reconstruct a single high-resolution image of an object from one or more measurement frames of that are blurred and noisy realizations of that object. The blind nature of MFBD algorithms permits the reconstruction process to proceed without having separate measurements or knowledge of the blurring functions in each of the measurement frames. This is accomplished by estimating the object common to all the measurement frames jointly with the blurring functions that are different from frame to frame. An issue of key importance is understanding how accurately the object pixel intensities can be estimated with the use of MFBD algorithms. Here we present algorithm-independent lower bounds to the variances of estimates of the object pixel intensities to quantify the accuracy of these estimates when the blurring functions are estimated pixel by pixel. We employ support constraints on both the object and the blurring functions to aid in making the inverse problem unique. The lower bounds are presented as a function of the sizes and shapes of these support regions and the number of measurement frames.