The impact of low signal-to-noise ratio values on the achievability of Cramér-Rao lower bounds with multi-frame blind deconvolution algorithms

Abstract

Cramer-Rao lower bound (CRB) theory can be used to calculate algorithm-independent lower bounds to the variances of parameter estimates. It is well known that the CRBs are achievable by algorithms only when the parameters can be estimated with sufficiently-high signal-to-noise ratios (SNRs). Otherwise, the CRBs are still lower bounds, but there can be a large gap between the CRBs and the variances that can be achieved by algorithms. We present results from our initial investigations into the SNR dependence of the achievability of the CRBs by multi-frame blind deconvolution (MFBD) algorithms for high-resolution imaging in the presence of atmospheric turbulence and sensor noise. With the use of sample statistics, we give examples showing that the minimum SNR value for which the CRBs can be achieved by our MFBD algorithm typically ranges between one and five, depending upon the strength of the prior knowledge used in the algorithm and the SNRs in the measured data.