Accurate and computationally efficient interpolation-based method for two-dimensional harmonic retrieval

Determining the frequencies of multiple resolvable exponentials is an important problem due to its application in diverse areas in science and engineering. In this paper, frequency estimation of two-dimensional (2-D) sinusoids is addressed. With the use of the periodogram in frequency domain, the required harmonics are first located coarsely. The characteristics of the 2-D spectrum is then analyzed, and the accurate estimates of the parameters are retrieved using an interpolation method iteratively. It is proved that at sufficiently high signal-to-noise ratio conditions, the harmonic estimates are asymptotically unbiased, and their variances are also analyzed. Furthermore, when only part of the data is observed, the proposed algorithm is tailored to get fast and accurate estimation results. Computer simulations are also included to compare the proposed approach with conventional 2-D harmonic retrieval schemes in terms of root mean square error performance and computational complexity.