基于RANSAC的压缩感知信号去噪
RANSAC-Based Signal Denoising Using Compressive Sensing
摘要：
在本文中，我们提出了一种方法来重建的信号表现出稀疏的变换域，有一些严重干扰的样本。这种稀疏驱动的信号恢复利用了一种精心设计的随机采样一致性（RANSAC）方法来选择样本的内点子集。为此，使用两个基本属性：信号样本表示稀疏系数的线性组合，而干扰降低原始信号的稀疏性。适当选择的样本进一步用作稀疏信号重构中的测量，使用来自压缩感测框架的算法执行。除了干扰降低变换域中的信号稀疏性这一事实之外，没有做出其他与干扰相关的假设-关于其统计行为或其值的范围没有特殊要求。作为一个案例研究，离散傅立叶变换（DFT）被认为是一个域的信号稀疏，由于其在信号处理理论和应用的重要性。数值结果有力地支持了所提出的理论。此外，还给出了重建信号信噪比的精确关系。这个简单的结果，方便地表征基于RANSAC的重建性能，数值证实了一组统计的例子。
英文摘要：
In this paper, we present an approach to the reconstruction of signals exhibiting sparsity in a transformation domain, having some heavily disturbed samples. This sparsity-driven signal recovery exploits a carefully suited random sampling consensus (RANSAC) methodology for the selection of an inlier subset of samples. To this aim, two fundamental properties are used: a signal sample represents a linear combination of the sparse coefficients, whereas the disturbance degrade original signal sparsity. The properly selected samples are further used as measurements in the sparse signal reconstruction, performed using algorithms from the compressive sensing framework. Besides the fact that the disturbance degrades signal sparsity in the transformation domain, no other disturbance-related assumptions are made -- there are no special requirements regarding its statistical behavior or the range of its values. As a case study, the discrete Fourier transform (DFT) is considered as a domain of signal sparsity, owing to its significance in signal processing theory and applications. Numerical results strongly support the presented theory. In addition, exact relation for the signal-to-noise ratio (SNR) of the reconstructed signal is also presented. This simple result, which conveniently characterizes the RANSAC-based reconstruction performance, is numerically confirmed by a set of statistical examples.
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