The question of signal-to-noise ratio (SNR) in intensity interferometry has been revisited in recent years, as researchers have realized that various innovations can offer significant improvements in SNR. These innovations include improved signal processing. Two such innovations, the use of positivity and the use of knowledge of the general shape of the object, have been proposed. This paper investigates the potential gains offered by these two approaches using Cramer-Rao lower bounds (CRLBs). The CRLB on the variance of the positivity-constrained maximum likelihood (ML) estimate is at best 1/4 of the variance of the unconstrained estimator. This is compared to the positivity-constrained ML estimator, which delivers a best-case variance reduction of only (1-1/π)/2=34.1%. The gains offered by prior knowledge depend on the quality of such information, as might be expected from optimal weighting of such data with the measured data. Furthermore, biases are induced by the application of constraints, and these biases can eliminate some or all of the advantage of lower variances, as found when considering the total root-mean-square error. A form of CRLB for variance is presented that properly incorporates prior information.
A new approach to the inversion problem of dynamical transmission electron diffraction is described, based on the method of generalized projections in set theory. An algorithm is described that projects between two sets of constrained scattering matrices. This iterative process can be shown to converge, giving the required structure factors (for some choice of origin) if the sets are convex. For the dynamical inversion problem, the set topology is that of an N 2 torus, the sets are not convex, and traps are therefore sometimes encountered. These can be distinguished from solutions, allowing the algorithm to be restarted until a solution is found. Examples of successful inversion from simulated multiple-scattering data are given, which therefore solve the phase problem of electron diffraction for centrosymmetric or noncentrosymmetric crystal structures. The method may also be useful for the three-beam X-ray diffraction problem.
Traditional blind deconvolution techniques rely on a statistical model that relates the measured data to the pristine scene whose reconstruction is sought. If the data is not consistent with this forward model, then the reconstruction is badly degraded. We develop a way of making blind deconvolution robust to modeling errors by assigning a weight to each pixel of measured data and iteratively updating the weights. We show that this approach is effective in several realistic modelmismatch scenarios.
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