Compressive sensing (CS) has emerged as a promising technique for collecting and reconstructing digital signals. In this article, we design a CS method for magnetic flux leakage (MFL) detectors based on the problem’s physics. A method is presented to reconstruct $x$ and $y$ components of magnetic $\overrightarrow {B}$ field using a few samples. First, the problem is formulated into an optimization framework where the goal is to minimize Euclidean distance between real and reconstructed signals while preserving the CS acquisition criteria. The resulting optimizations are then simplified and solved through the established majorization minimization (MM) method. Meanwhile, a Gaussian sampling strategy is adopted where samples with more information have a higher chance of being selected. Validation of the proposed method is accomplished through the performance comparison among the proposed method and several established high-performance CS techniques on gathered experimental data. The extensive validation of the signals gathered from 17 artificial defects on the 12-m pipe reveals that the signals can be compressed and recovered with exceptional fidelity when the problem’s physical structure is known.

中文翻译：

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磁通量泄漏探测器的结构感知压缩传感：理论和实验验证

压缩感知 (CS) 已成为收集和重建数字信号的有前途的技术。在本文中，我们根据问题的物理原理设计了一种用于漏磁 (MFL) 检测器的 CS 方法。提出了一种重构方法 $x$ 和 $y$ 磁性元件 $\overrightarrow {B}$ 场使用几个样本。首先，问题被表述为一个优化框架，其目标是最小化真实信号和重建信号之间的欧几里德距离，同时保留 CS 采集标准。然后通过已建立的专业化最小化 (MM) 方法简化和解决由此产生的优化。同时，采用高斯采样策略，信息越多的样本被选中的机会越大。所提出的方法的验证是通过所提出的方法与几种已建立的高性能 CS 技术在收集的实验数据上的性能比较来完成的。