Fast algorithms for multidimensional harmonic retrieval

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Classic multidimensional harmonic retrieval is crucial for various applications, including sensor array processing, radar, mobile communications, and nuclear magnetic resonance spectroscopy. Recent parametric subspace approaches, particularly ESPRIT-based algorithms, are favored for their computational efficiency and straightforward implementation. These algorithms leverage shift invariances in measurements to estimate parameters by solving a joint eigenvalue problem. However, when measurements are uniformly sampled across dimensions, ESPRIT methods often fail to utilize all available information, leading to performance losses in parameter estimation. This work proposes a novel approach to multidimensional harmonic retrieval by parameterizing the estimation of harmonics separately along different dimensions. This method avoids the computational burden of optimizing a multidimensional cost function, making the problem more tractable while preserving the advantages of multidimensional measurement data, such as improved uniqueness conditions and resolution. New matrix rank and polynomial rooting criteria are developed to estimate parameters across dimensions. The proposed rank criteria are interpreted in various contexts, yielding new stochastic uniqueness conditions and efficient parameter association strategies. Additionally, a connection between ESPRIT-type methods and root-MUSIC approaches is established, allowing the ran