An Algorithm-independent Analysis of the Quality of Images Produced Using Multi-frame Blind Deconvolution Algorithms

In many imaging applications, it is desired to reconstruct a high-resolution image of an object from one or more blurred and noisy measured data frames. A key component of the reconstruction process is deconvolving the blurring point spread functions (PSFs) from the measured data frames. When the blurring PSFs are known a priori or can be measured separately to the desired degree of accuracy, the deconvolution process is straightforward. However, in many situations, the blurring PSFs are both not known a priori and there are no separate measurements of them. One such situation is imaging through atmospheric turbulence where the measured data frames are a sequence of one or more short-exposure images and the atmospheric turbulence blurring is not known and is different for each data frame. For these situations, the blurring PSFs must be estimated jointly with the object from the measured data frames. Algorithms that carry out this joint estimation process are known as multi-frame blind deconvolution (MFBD) algorithms. It is of interest to determine the fundamental limits (i.e., algorithm-independent limits) to the achievable resolution and noise reduction in MFBD reconstructions. Cram?r-Rao lower bound (CRB) theory can be used to generate these limits. In this presentation we give results from applying CRB theory to the single-frame and multi-frame blind deconvolution problem. We calculate these fundamental limits for a variety of scenarios, including Zernike versus pixel-based PSF estimation, the number of frames used, the texture of the object and PSFs, photon versus read noise, and the sizes of the support constraints. Some of the results we show include the fact that Zernike-based PSF estimation produces higher-quality images than does pixel-based PSF estimation, the amount of noise reduction is an increasing function of PSF texture, and the benefit of adding just a few frames of data is greater for highly-textured PSFs but is independent of PSF texture when more than ~ five frames are used.