Adaptive Graph-based Total Variation for Tomographic Reconstructions

TL;DR

This paper introduces Adaptive Graph-based Total Variation (AGTV), a novel method for tomographic image reconstruction that connects similar regions across the entire image, improving texture preservation and computational efficiency over existing local and non-local TV methods.

Contribution

The paper proposes AGTV, a computationally efficient, adaptive graph-based regularization method that enhances texture preservation by globally connecting similar regions during reconstruction.

Findings

AGTV outperforms local TV in texture preservation.

AGTV is more computationally efficient than NLTV.

AGTV effectively promotes sparsity in multiple domains.

Abstract

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.