盲多带信号重构：模拟信号的压缩感知
Blind Multi-Band Signal Reconstruction: Compressed Sensing for Analog Signals
摘要：
我们解决的问题，重建一个多频带信号从其子奈奎斯特逐点采样。到目前为止，所有的重建方法提出了这类信号假设的频带位置的知识。在本文中，我们提出了一种非线性盲多带信号的完美重建方案，它不需要频带的位置。我们的方法假设现有的盲多陪集采样方法。利用多带信号在连续频域中的稀疏结构，将连续重构问题转化为单个有限维问题，无需离散化。由此产生的问题，可以制定的压缩传感的框架内，因此可以有效地解决使用已知的易于处理的算法，从这个新兴的领域。我们还开发了盲信号重建所需的平均采样率的理论下限，这是已知频谱恢复的最小速率的两倍。我们的方法确保了完美的重建广泛的一类以最小速率采样的信号。数值实验演示盲采样和重建的最小采样率。
英文摘要：
We address the problem of reconstructing a multi-band signal from its sub-Nyquist point-wise samples. To date, all reconstruction methods proposed for this class of signals assumed knowledge of the band locations. In this paper, we develop a non-linear blind perfect reconstruction scheme for multi-band signals which does not require the band locations. Our approach assumes an existing blind multi-coset sampling method. The sparse structure of multi-band signals in the continuous frequency domain is used to replace the continuous reconstruction with a single finite dimensional problem without the need for discretization. The resulting problem can be formulated within the framework of compressed sensing, and thus can be solved efficiently using known tractable algorithms from this emerging area. We also develop a theoretical lower bound on the average sampling rate required for blind signal reconstruction, which is twice the minimal rate of known-spectrum recovery. Our method ensures perfect reconstruction for a wide class of signals sampled at the minimal rate. Numerical experiments are presented demonstrating blind sampling and reconstruction with minimal sampling rate.
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