Model-based approaches to imaging, like specialized image enhancements in astronomy, facilitate explanations of relationships between observed inputs and computed outputs. These models may be expressed with extended matrix-vector (EMV) algebra, especially when they involve only scalars, vectors, and matrices, and with n-mode or index notations, when they involve multidimensional arrays, also called numeric tensors or, simply, tensors. While this paper features an example, inspired by exoplanet imaging, that employs tensors to reveal (inverse) 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 a dual-variant index notation, with Einstein summation convention, and codesigned object-oriented software, called the RTToolbox for MATLAB. Extensions to Ricci notation offer novel representations for entrywise, pagewise, and broadcasting operations popular in EMV frameworks for imaging. Complementing the EMV algebra computable with MATLAB, the RTToolbox demonstrates programmatic and computational efficiency via careful design of numeric tensor and dual-variant index classes. Compared to its closest competitor, also a numeric tensor framework that uses index notation, the RT framework enables superior ways to model imaging problems and, thereby, to develop solutions.

翻译：基于模型的成像方法，例如天文学中的专用图像增强，有助于解释观测输入与计算输出之间的关系。这些模型可以用扩展矩阵-向量（EMV）代数表示，尤其是当仅涉及标量、向量和矩阵时；当涉及多维数组（也称为数值张量或简称为张量）时，则可以用n模或索引表示法表示。尽管本文以系外行星成像为灵感，展示了一个示例，该示例在图像增强模型中使用张量揭示（逆）二维快速傅里叶变换，但实际工作是关于可用于基于模型成像的张量代数和软件（即张量框架）。本文提出了一个里奇符号张量（RT）框架，包括双变体索引表示法（采用爱因斯坦求和约定）和协同设计的面向对象软件（称为用于MATLAB的RTToolbox）。里奇符号的扩展为EMV框架中的逐元素、逐页面和广播操作提供了新颖的表示形式，这些操作在成像中常用。作为MATLAB可计算的EMV代数的补充，RTToolbox通过精心设计数值张量和双变体索引类，展示了程序性和计算效率。与其最接近的竞争对手（也是一个使用索引表示法的数值张量框架）相比，RT框架能够以更优的方式对成像问题进行建模，从而开发出解决方案。