论文标题
基于RANSAC的信号使用压缩传感
RANSAC-Based Signal Denoising Using Compressive Sensing
论文作者
论文摘要
在本文中，我们提出了一种在转化域中表现出稀疏性的信号的重建方法，其中有一些严重的样本。这种稀疏驱动的信号恢复利用了精心适合的随机采样共识（RANSAC）方法，用于选择样品的嵌入式子集。为此，使用了两个基本属性：信号样本表示稀疏系数的线性组合，而干扰降低了原始信号稀疏性。正确选择的样品进一步用作稀疏信号重建中的测量，并使用来自压缩传感框架的算法进行。除了扰动降低转换域中信号稀疏性的事实外，没有做出其他与干扰有关的假设 - 关于其统计行为或其值范围没有特殊要求。作为一个案例研究，由于其在信号处理理论和应用中的重要性，离散的傅立叶变换（DFT）被认为是信号稀疏的域。数值结果强烈支持所提出的理论。另外，还介绍了重建信号的信噪比（SNR）的确切关系。这一简单的结果可方便地表征了基于RANSAC的重建性能，它通过一组统计示例在数值上证实。
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.
