Constrained least squares estimation incorporating wavefront sensing

We address the optimal processing of astronomical images using the deconvolution from wave-front sensing technique (DWFS). A constrained least-squares (CLS) solution which incorporates ensemble-averaged DWFS data is derived using Lagrange minimization. The new estimator requires DWFS data, noise statistics, optical transfer function statistics, and a constraint. The constraint can be chosen such that the algorithm selects a conventional regularization constant automatically. No ad hoc parameter tuning is necessary. The algorithm uses an iterative Newton-Raphson minimization to determine the optimal Lagrange multiplier. Computer simulation of a 1m telescope imaging through atmospheric turbulence is used to test the estimation scheme. CLS object estimates are compared with the corresponding long exposure images. The CLS algorithm provides images with superior resolution and is computationally inexpensive, converging to a solution in less than 10 iterations.