Generalized rectification in the L1-norm with application to robust array processing

We present in this paper a multiple linear regression scheme in the L₁-norm which operates on the array output covariance matrix. The proposed method rectifies the covariance matrix by exploiting the structural properties resulting from the array geometry. In the case of a defective sensor, it is able to fully restore the covariance which would be observed if all sensors were working correctly. Simulations in Direction Of Arrival estimation with a uniform circular array demonstrate the interest of this L₁ approach compared to conventional L₂ techniques.