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An innovative method for the synthesis of maximally sparse linear arrays matching arbitrary reference patterns is proposed. In the framework of sparseness constrained optimization, the approach exploits the multi-task (MT) Bayesian compressive sensing (BCS) theory to enable the design of complex non-Hermitian layouts with arbitrary radiation and geometrical constraints. By casting the pattern matching problem into a probabilistic formulation, a Relevance-Vector-Machine (RVM) technique is used as solution tool. The numerical assessment points out the advances of the proposed implementation over the extension to complex patterns of and it gives some indications about the reliability, flexibility, and numerical efficiency of the MT-BCS approach also in comparison with state-of-the-art sparse-arrays synthesis methods.