Structure-aware Compressive Sensing for Magnetic Flux Leakage Detectors: Theory and Experimental Validation

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.