Evaluation of a Maximum-likelihood Based Multi-frame Blind Deconvolution Algorithm Using Cramer-rao Bounds

Recently, Cramer-Rao bound (CRB) theory for support-constrained multi-frame blind deconvolution has been developed. In this paper, this CRB theory is employed as a metric to evaluate the performance of a multi-frame blind-deconvolution (MFBD) imaging algorithm developed at the Air Force Maui Optical and Supercomputing Site, a site operated by the Air Force Research Laboratory. Sample variances from the MFBD algorithm named PCID (physically constrained blind deconvolution) and CRB lower bounds to variances are compared for a baseline imaging scenario that employs an object, blurring, and noise model. The variance reduction effects produced by imposing support constraints on the object and on the point spread function (PSF) are analyzed. Pixel-by-pixel sample variance maps are compared to CRB maps for the case of perfect and loose object support constraints. The PCID sample variance maps are evaluated against CRBs both to determine the relative magnitude of these variances as opposed to CRB lower bounds and to assess overall morphology differences. For the baseline imaging scenario, the PCID pixel-by-pixel sample variance magnitudes match their associated CRBs, and the PCID sample variances and CRBs share the same overall morphology. Additionally, PCID sample variance results are presented for cases where the baseline imaging and post-processing scenario above is extended beyond where CRB theory has been developed. Extensions to the model scenario include the use of: positivity in the imaging algorithm, Fourier-domain and Tikhonov regularization, and the addition of photon noise in the imaging model. The matching PCID and CRB results from above are used as a basis for comparison with these sample variance results.