Model-based image reconstruction by means of a constrained least-squares solution

The problem of the optimal use of object model information in image reconstruction is addressed. A closed-form solution for the estimated object spectrum is derived with the Lagrange multiplier technique, which assumes a measured image, knowledge of the optical transfer function, statistical information about the measurement noise, and a model of the object. This reconstruction algorithm is iterative in nature because the optimal Lagrange multiplier is not generally known at the start of the problem. We derive the estimator, describe one technique for determining the optimal Lagrange multiplier, demonstrate a stopping criterion based on the mean-square error between a noise-free image and the photon-limited version of the image, and show representative results for both filled- and sparse-aperture imaging applications.