Unit interval vector recovery from sparse measurements for eddy current defect imaging

Traditional raster scanning methods for defect imaging require sampling at more than twice the spatial frequency to achieve the desired spatial resolution. This study presents a new approach for defect imaging that uses spatially sparse measurements, significantly reducing the number of samples needed compared to the Nyquist rate. In this method, defects in a metal slab are modeled as perturbations in material properties. Perturbation analysis is applied to the eddy current system to establish a linear relationship between the measured magnetic flux density (MFD) and the material properties. This relationship forms a linear system where the solution is a vector with entries within the range [0, 1]. To recover this vector from a limited number of measurements, a probabilistic method is employed. A beta prior is applied to the vector to enforce the unit interval constraint, and a variational approximation of the posterior probability, conditioned on the measurements, is computed. The proposed framework is evaluated using both simulated and experimental data to image defects in a metal plate. The results demonstrate that the method can image defects as small as 2 mm with a sensor spacing of 4 mm, significantly surpassing the resolution limits imposed by the Nyquist theorem.