Controlling TV Regularization with Deep Learning

Abstract

Tomography reconstruction is ill posed, thus regularization is needed to avoid overfitting. Total variation regularization modifies the maximum-likelihood objective by penalizing high variation solutions. The strength of regularization, called the regularization parameter, is usually set manually, because there is no straightforward method to find its optimal value. If the regularization parameter is too small, the reconstruction will be noisy. If it is too strong, the true signal is compromised and painted like or checkerboard pattern artifacts may show up. This paper proposes the application of deep learning techniques to control the regularization parameters dynamically during the reconstruction process. That is, the regularization parameter is automatically set and is modified in each iteration cycle to improve convergence. Unlike other techniques, we replace none of the components of the reconstruction algorithm by a trained neural network, but control the parameter of the TV-regularized ML-EM algorithm. Thus, reasonably sized training set can also lead to robust and efficient solutions. The algorithm is demonstrated for a 2D test scenario.