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 a subset of inlier samples. To this aim, two fundamental properties are used: A signal sample represents a linear combination of the sparse coefficients, whereas the disturbance degrades the 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 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, the exact relation for the signal-to-noise ratio 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.

在本文中，我们提出了一种重建在变换域中表现出稀疏性的信号的方法，这些信号具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适合的随机采样一致性 (RANSAC) 方法来选择内部样本的子集。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，而干扰会降低原始信号的稀疏性。正确选择的样本进一步用作稀疏信号重建中的测量，使用来自压缩传感框架的算法执行。除了干扰降低了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——对其统计行为或其值的范围没有特殊要求。作为案例研究，离散傅立叶变换被认为是信号稀疏域，因为它在信号处理理论和应用中具有重要意义。数值结果强烈支持所提出的理论。此外，还给出了重构信号信噪比的确切关系。这个简单的结果可以方便地表征基于 RANSAC 的重建性能，并通过一组统计示例在数值上得到证实。数值结果强烈支持所提出的理论。此外，还给出了重构信号信噪比的确切关系。这个简单的结果可以方便地表征基于 RANSAC 的重建性能，并通过一组统计示例在数值上得到证实。数值结果强烈支持所提出的理论。此外，还给出了重构信号信噪比的确切关系。这个简单的结果可以方便地表征基于 RANSAC 的重建性能，并通过一组统计示例在数值上得到证实。