Randomized second-order algorithm for MAP estimation and fast MSE estimator applied to Computed Tomography
Two families of algorithms for MAP and MSE estimation respectively will be presented and applied to a monoenergetic X-ray Computed Tomography (CT) acquisition model.
Second order methods for solving regularized optimization problems with generalized linear models have been widely studied but despite the superior convergence rate compared to first order methods one weakness relies on the computational cumbersome for calculating the Hessian matrix. Additionally, in imaging applications where the input prior is difficult to model, powerful regularization techniques are based on data-driven models or denoisers.
For MAP estimation, an efficient and accurate randomized second order method for model based CT reconstruction is proposed. The algorithm combines the idea of dimensionality reduction of the Hessian of the likelihood cost function by sketching, using ridge leverage scores, and an explicit regularizer term which can be implemented by a generic denoiser through the score matching formulation. We show how to compute the gradient and the Hessian of the likelihood and regularizer together with simulated results.
Finally, a fist order iterative method, called approximate message passing, will be presented for performing MSE estimation efficiently.