Adaptive Graph-based Total Variation for Tomographic Reconstructions
This work addresses texture preservation and artefact reduction in tomographic imaging, offering a generalization of sparsity-exploiting reconstruction methods, though it appears incremental as it builds on non-local TV approaches.
The paper tackles the problem of over-smoothing and artefact creation in tomographic reconstructions by proposing Adaptive Graph-based Total Variation (AGTV), which establishes connections between similar regions across the entire image and updates the graph prior iteratively, resulting in a computationally efficient method that promotes sparsity in wavelet and graph gradient domains.
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 artefacts due to over-smoothing. Non-Local TV (NLTV) methods have been proposed as a solution to this but they either lack continuous updates due to computational constraints or limit the locality to a small region. In this paper, we propose Adaptive Graph-based TV (AGTV). The proposed method goes beyond spatial similarity between different regions of an image being reconstructed by establishing a connection between similar regions in the entire image regardless of spatial distance. As compared to NLTV the proposed method is computationally efficient and involves updating the graph prior during every iteration making the connection between similar regions stronger. Moreover, it promotes sparsity in the wavelet and graph gradient domains. Since TV is a special case of graph TV the proposed method can also be seen as a generalization of SER and TV methods.