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A new algorithm based on semidefinite programming is presented for estimation of distributed source fields measured through a sensor array. The problem can be viewed as a subclass of inverse problems, which have been extensively investigated in the literature. Our approach is based on the so called information based complexity (IBC) paradigm, which formalizes the notion of seeking the set of all solutions that are consistent with the observed data. We formulate our problem as a question of estimating the source up to a prespecified resolution (average source field in a neighborhood) from the observed data with optimal accuracy. We show that this problem is convex and can be reformulated as a semidefinite program.