Phase-Transition Behavior in Array Diagnosis Using Sparse Recovery Techniques

The aim of this contribution is an analysis the the probability of correct estimation of the faulty elements using a measurement strategy similar to the one-pixel camera. The set-up is based on a reflectarray whose scattering elements are electronically controlled. Numerical simulations shows a phase-transition behavior of the probability of AUT fault detection using the proposed measurement set-up, based on compressed sensing-sparse recovery strategy. The important practical consequence is that, for a given degrees of sparsity of the unknown vector (i.e. for any fixed maximum number of defects) and for a given noise level, it is possible to identify the exact number of measurements needed to perform a correct array diagnosis.