Compressive-sensing based super-resolution detection for leakage and uniform blockage in water pipelines

Abstract Reflectometry techniques for water pipeline defect detection suffer from low resolution problems since only low frequency waves can travel long distances in pipeline systems. In this paper, a method for estimating the super-resolved impulse response (IR) of the system from reflectometry measurements is established using a gridless compressive sensing (CS) framework. The proposed method provides super-resolution results by reconstructing the sparse IR consisting of a series of delta ( δ ) functions, whose time delays and amplitudes are estimated by solving the dual problem of CS optimization. The unique reconstruction of IR is guaranteed by a minimum separation between adjacent δ functions, which closely relates to IR sparsity. This minimum separation requirement is validated theoretically, using the restricted isometry property, and numerically. It is proven that the IR of two discrete defects spaced less than a quarter of the minimum observation wavelength can be uniquely reconstructed with super-resolution. Systematic simulations and laboratory experiments show that the proposed method precisely recovers the IR of uniform blockages and leakages in water pipelines when the minimum separation is satisfied. With super-resolution IR, closely spaced blockage edges and leakages can be well distinguished and precisely localized. The size of both blockages and leakage holes can also be estimated with millimeter level accuracy.