Bayesian image reconstruction from partial image and aliased spectral intensity data

摘要

An image reconstruction problem motivated by xrayfiber diffraction analysis is considered. The experimental dataare sums of the squares of the amplitudes of particular sets ofFourier coefficients of the electron density, and a part of theelectron density is known. The image reconstruction problem is toestimate the unknown part of the electron density, the “image.”A Bayesian approach is taken in which a prior model for theimage is based on the fact that it consists of atoms, i.e., theunknown electron density consists of separated, sharp peaks.Currently used heuristic methods are shown to correspond tocertain maximum a posteriori estimates of the Fourier coefficients.An analytical solution for the Bayesian minimum mean-squareerrorestimate is derived. Simulations show that the minimummean-square-error estimate gives good results, even when thereis considerable data loss, and out-performs the maximum aposteriori estimates.