引导信号重构理论
Guided Signal Reconstruction Theory
摘要：
一个公理化的方法来信号重建制定，涉及一个样本一致集和指导集，描述所需的重建。提出了一种新的无帧重建方法，即重建集的概念，重建集定义为样本一致集和引导集之间的最短路径。在Hilbert空间中研究了重建集的存在性和唯一性，其中引导集是一个闭子空间，样本一致集是由一个采样子空间构成的一个闭平面.连接到以前已知的一致，广义和正则化重建澄清。新的稳定性和重建误差界的推导，使用采样和引导子空间之间的最大非平凡的角度。提出了共轭梯度迭代重建算法，并给出了数值例子。
英文摘要：
An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a reconstruction set, defined as a shortest pathway between the sample consistent set and the guiding set. Existence and uniqueness of the reconstruction set are investigated in a Hilbert space, where the guiding set is a closed subspace and the sample consistent set is a closed plane, formed by a sampling subspace. Connections to earlier known consistent, generalized, and regularized reconstructions are clarified. New stability and reconstruction error bounds are derived, using the largest nontrivial angle between the sampling and guiding subspaces. Conjugate gradient iterative reconstruction algorithms are proposed and illustrated numerically for image magnification.
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