Ricci-Notation Tensor Framework for Model-Based Approaches to Imaging

Model-based approaches to imaging, like specialized image enhancements in astronomy, favour physics-based models which facilitate explanations of relationships between observed inputs and computed outputs. While this paper features a tutorial example, inspired by exoplanet imaging, that reveals embedded 2D fast Fourier transforms in an image enhancement model, the work is actually about the tensor algebra and software, or tensor frameworks, available for model-based imaging. The paper proposes a Ricci-notation tensor (RT) framework, comprising an extended Ricci notation, which aligns well with the symbolic dual-index algebra of non-Euclidean geometry, and codesigned object-oriented software, called the RTToolbox for MATLAB. Extensions offer novel representations for entrywise, pagewise, and broadcasting operations popular in extended matrix-vector (EMV) frameworks for imaging. Complementing the EMV algebra computable with MATLAB, the RTToolbox demonstrates programmatic and computational efficiency thanks to careful design of tensor and dual-index classes. Compared to a numeric tensor predecessor, the RT framework enables superior ways to model imaging problems and, thereby, to develop solutions.