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In this paper, a novel antenna array diagnostic approach is presented. The failures in antenna arrays are detected by means of a non-Hilbertian Lebesgue-space <inline-formula> <tex-math notation="LaTeX">$L^{p}$ </tex-math></inline-formula> technique to solve the underlying inverse problem. The solution of this inverse problem enables to retrieve the distribution of faulty feed excitations of the antenna under test starting from far-field measurements. The developed approach has been numerically validated. Simulations concern planar arrays where different rates and distributions of failures have been tested. Results show good capabilities in detecting damaged regions in the analyzed scenarios.