A hybrid non-convex compressed sensing approach for array diagnosis using sparse promoting norm with perturbation technique

The use of ℓ_p (0 < p < 1) norm minimization will improve array diagnosis performance provided that the issue of local minima associated to its non-convex nature is properly handled. In order to overcome this deficiency, a hybrid method using random perturbation and non-convex optimization is investigated in this paper. Although it acquires a higher computational time, the trade-off between an accurate diagnosis and the computational burden appears to be acceptable. Theoretical analysis and simulation results demonstrate that the proposed method overcomes this disadvantage effectively and achieves better performance compared to the standard ℓ₁ norm minimization with a smaller number of far-field measurements, suggesting that the proposed method can be used to improve the performance of array diagnosis.