Fast non-convex compressed sensing approach for diagnosis of defective array elements using planar near-field measurements

The array diagnosis method using random perturbation-convex local minimiser has to make a compromise between the probability of correct reconstruction and the computational burden. In order to overcome this limitation, in this study, a nonconvex l(p) (0 < p < 1) norm minimisation utilising iteratively reweighted least squares algorithm for identification of impaired planar array elements is investigated. Taken into account that the number of failed elements is far less than the total array elements, the differential array composed of the healthy array and damaged array is constructed. Then the near-field data are acquired by the probe using a random under-sampling strategy. Finally, the sparse excitations of this array are estimated through the proposed algorithm and the goal of failure detection is achieved. Numerical simulation results indicate that the proposed approach lowers the mean square error of retrieved excitations compared to the non-convex approach using perturbation technique, with the advantage of a significant reduction of running time. In addition, it also improves the probability of success rate of diagnosis effectively compared to the l 1 norm and reweighted l 1 norm regularised methods.