Sparse-View CT Reconstruction Using Curvelet and TV-Based Regularization

Abstract

The reconstruction from sparse-view projections is one of important problems in computed tomography limited by the availability or feasibility of a large number of projections. Total variation (TV) approaches have been introduced to improve the reconstruction quality by smoothing the variation between neighboring pixels. However, the TV-based methods for images with textures or complex shapes may generate artifacts and cause loss of details. Here, we propose a new regularization model for CT reconstruction by combining regularization methods based on TV and the curvelet transform. Combining curvelet regularizer, which is optimally sparse with better directional sensitivity than wavelet transforms with TV on the other hand will give us a unique regularization model that leads to the improvement of the reconstruction quality. The split-Bregman (augmented Lagrangian) approach has been used as a solver which makes it easy to incorporate multiple regularization terms including the one based on the multiresolution transformation, in our case curvelet transform, into optimization framework. We compare our method with the methods using only TV, wavelet, and curvelet as the regularization terms on the test phantom images. The results show that there are benefits in using the proposed combined curvelet and TV regularizer in the sparse view CT reconstruction.