We introduce a reconstruction framework that can account for shape related a priori information in ill-posed linear inverse problems in imaging. It is a variational scheme that uses a shape functional defined using deformable templates machinery from shape theory. As proof of concept, we apply the proposed shape based reconstruction to 2D tomography with very sparse measurements, and demonstrate strong empirical results.

中文翻译：

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使用线性变形进行基于形状的图像重建


我们引入了一种重建框架，可以解释成像中不适定线性逆问题中与形状相关的先验信息。它是一种变分方案，使用形状函数，该形状函数是使用形状理论中的可变形模板机制定义的。作为概念证明，我们将所提出的基于形状的重建应用于具有非常稀疏测量的二维断层扫描，并展示了强有力的经验结果。