Adaptive Graph-based Total Variation for Tomographic Reconstructions

Sparsity exploiting image reconstruction (SER) methods have been extensively used with Total Variation (TV) regularization for tomographic reconstructions. Local TV methods fail to preserve texture details and often create additional artifacts due to over-smoothing. Non-Local TV (NLTV) has been proposed as a solution to this but lacks continuous update and is computationally complex. In this paper we propose Adaptive Graph-based TV (AGT). Similar to NLTV our proposed method goes beyond spatial similarity between different regions of an image being reconstructed by establishing a connection between similar regions in the image regardless of spatial distance. However, it is computationally more efficient and involves updating the graph prior during every iteration making the connection between similar regions stronger. Since TV is a special case of graph TV the proposed method can also be seen as a generalization of SER and TV methods. It promotes sparsity in the wavelet and graph gradient domains. Extensive experimentation shows that when compared to other methods we achieve a better result with AGT in every case.