Fast conjugate gradient algorithm extension for analyzer-based imaging reconstruction

This paper presents an extension of the classic Conjugate Gradient Algorithm. Motivated by the Analyzer-Based Imaging inverse problem, the novel method maximizes the Poisson regularized log-likelihood with a non-linear transformation of parameter faster than other solutions. The new approach takes advantage of the special properties of the Poisson log-likelihood to conjugate each ascend direction with respect all the previous directions taken by the algorithm. Our solution is compared with the general solution for non-quadratic unconstrained problems: the Polak- Ribiere formula. Both methods are applied to the ABI reconstruction problem.