Low-Rank Modeling of Local Sinogram Neighborhoods with Tomographic Applications

Abstract

Previous work has demonstrated that Fourier imaging data will often possess multifold linear shift-invariant autoregression relationships. This autoregressive structure is useful because it enables missing data samples to be imputed as a linear combination of neighboring samples, and also implies that certain structured matrices formed from the data will have low rank characteristics. The latter observation has enabled a range of powerful structured low-rank matrix recovery techniques for reconstructing sparsely-sampled and/or low-quality data in Fourier imaging modalities like magnetic resonance imaging. In this work, we demonstrate theoretically and empirically that similar modeling principles also apply to sinogram data, and demonstrate how this can be leveraged to restore missing information from real high-resolution X-ray imaging data from an integrated circuit.