Sparse-View Image Reconstruction in Cone-Beam Computed Tomography with Variance-Reduced Stochastic Gradient Descent and Locally-Adaptive Proximal Operation

There is a growing interest in image reconstruction from a small number of projections for computed tomography. Most of the available algorithms require a large number of iterations to reconstruct a high-quality image and they include parameters that need careful tuning. In this paper, we present a new algorithm that aims at reducing these problems. We formulate the reconstruction as an unconstrained optimization problem that consists of a measurement consistency term and a total variation regularization. The algorithm that we propose is based on the class of proximal gradient methods. Since the basic proximal gradient method is slow, we propose three modifications to improve its convergence speed. First, instead of proximal gradient iterations, we use a variance-reduced stochastic proximal gradient descent updates. Second, we apply the proximal operator with a locally adaptive regularization parameter; specifically, we partition the image into small blocks and denoise each block with a regularization parameter that depends on the probability of the presence of important image features in that block. Thirdly, at each iteration of the algorithm, we minimize the objective function over the subspace spanned by the current proximal gradient update and several previous update directions. The step size in the stochastic proximal gradient descent can be set equal to one and we suggest an easy method to find a small range that contains the acceptable values for the regularization parameter. Our experiments show that the proposed algorithm can recover a high-quality image from undersampled projections in a small number of iterations.