连续帧随机信号处理
Randomized Signal Processing with Continuous Frames
摘要：
本文重点介绍信号处理任务，其中信号从信号空间转换到一个更高维的系数空间（也称为相空间）使用连续帧，在系数空间中处理，并合成到一个输出信号。我们展示了如何近似这样的方法，称为相空间信号处理方法，使用蒙特卡罗方法。与连续标架的标准离散化方法不同，本文提出的蒙特卡罗方法是基于从连续系统中采样离散标架的方法，直接对连续标架进行正交逼近。我们表明，蒙特卡罗方法允许工作与高度冗余的连续帧，因为一定的精度所需的样本的样本个数是成比例的信号空间的尺寸，而不是相空间的尺寸。此外，即使连续框架是高度冗余的，蒙特卡罗样本也是均匀分布的，因此比标准框架离散化更忠实地表示系数空间。
英文摘要：
This paper focuses on signal processing tasks in which the signal is transformed from the signal space to a higher dimensional coefficient space (also called phase space) using a continuous frame, processed in the coefficient space, and synthesized to an output signal. We show how to approximate such methods, termed phase space signal processing methods, using a Monte Carlo method. As opposed to standard discretizations of continuous frames, based on sampling discrete frames from the continuous system, the proposed Monte Carlo method is directly a quadrature approximation of the continuous frame. We show that the Monte Carlo method allows working with highly redundant continuous frames, since the number of samples required for a certain accuracy is proportional to the dimension of the signal space, and not to the dimension of the phase space. Moreover, even though the continuous frame is highly redundant, the Monte Carlo samples are spread uniformly, and hence represent the coefficient space more faithfully than standard frame discretizations.
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