论文标题
基于电视的定期功能重建
TV-based Reconstruction of Periodic Functions
论文作者
论文摘要
我们介绍了一个通用框架，以重建有限的许多且可能是嘈杂的线性测量值的周期性多元函数。重构任务被提出为受惩罚的凸优化问题，以凸数据保真度功能和稀疏性促进性的基于总变化的总惩罚之间的形式，涉及适当的固定型正规化操作员L。在这种情况下，我们在定期衡量的情况下，表明与周期性的衡量标准相比，我们更加衡量了一个定期的lots。主要结果是针对最广泛的测量功能，样条加入的操作员和凸数据保真功能的。我们为各种正则化运算符和测量类型（例如，空间采样，傅立叶采样或方形积分函数）举例说明了我们的结果。我们还考虑了单变量和多变量周期函数的重建。
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking the form of a sum between a convex data fidelity functional and a sparsity-promoting total variation based penalty involving a suitable spline-admissible regularizing operator L. In this context, we establish a periodic representer theorem, showing that the extreme-point solutions are periodic L-splines with less knots than the number of measurements. The main results are specified for the broadest classes of measurement functionals, spline-admissible operators, and convex data fidelity functionals. We exemplify our results for various regularization operators and measurement types (e.g., spatial sampling, Fourier sampling, or square-integrable functions). We also consider the reconstruction of both univariate and multivariate periodic functions.
