The ESPRIT method is a classical method for one-dimensional harmonic retrieval. During the past two decades it has become apparent that several applications in signal processing correspond to the less studied Multi-dimensional Harmonic Retrieval (MHR) problem. In order to accommodate this demand, we propose an extension of ESPRIT to MHR based on the coupled canonical polyadic decomposition. This leads to a dedicated uniqueness condition and an algebraic framework for MHR.
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