New algorithms for maximum entropy image restoration

We present two new algorithms for image restoration by the maximum entropy method, both based on the preconditioned conjugate gradient method for linear equations. They are simple, robust, and well suited for vector processing. We find that they converge more quickly than the standard Cambridge algorithm, as a function of the total number of search directions, while the computation time per search direction is roughly the same. An important part of both algorithms is a simple and reasonably accurate formula for estimating the Lagrange multiplier in the basic equation. Another important part of the main algorithm is the guarding against negative pixel values by reduction of components of search directions. The second algorithm can be run without the entropy term and without preconditioning to give a solution resembling the maximum entropy solution.