A fully linearized ADMM algorithm for optimization based image reconstruction

Optimization based image reconstruction algorithm is an advanced algorithm in medical imaging. However, the corresponding solving algorithm is challenging because the model is usually large-scale and non-smooth. This work aims to devise a simple and convergent solver for optimization model.

The alternating direction method of multipliers (ADMM) algorithm is a simple and effective solver of the optimization model. However, there always exists a sub-problem that has not close-form solution. One may use gradient descent algorithm to solve this sub-problem, but the step-size selection via line search is time-consuming. Or, one may use fast Fourier transform (FFT) to get a close-form solution if the sparse transform matrix is of special structure. In this work, we propose a fully linearized ADMM (FL-ADMM) algorithm that avoids line search to determine step-size and applies to sparse transform of any structure.

We derive the FL-ADMM algorithm instances for three total variation (TV) models in 2D computed tomography (CT). Further, we validate and evaluate one FL-ADMM algorithm and explore how two important factors impact convergence rate. These studies show that the FL-ADMM algorithm may accurately solve the optimization model.

The FL-ADMM algorithm is a simple, effective, convergent and universal solver of optimization model in image reconstruction. Compared to the standard ADMM algorithm, the new algorithm does not need time-consuming step-size line-search or special demand to sparse transform. It is a rapid prototyping tool for optimization based image reconstruction.