High-resolution estimation of multidimensional spectra from unevenly sampled data

Estimation of high-resolution multidimensional spectra from unevenly sampled limited sized data sets plays an important role in a large variety of signal processing applications. In this work, we develop a high-resolution non-parametric estimator for unevenly sampled N-dimensional data based on a recently introduced iterative method, the so-called iterative adaptive approach (IAA). The proposed estimator uses the definition of the multidimensional Fourier transform to obtain a frequency domain representation of the unevenly sampled signal. Using tensor algebra, the multidimensional frequency domain representation is then recast into matrix format and used in a weighted least squares (WLS) fitting criterion to iteratively obtain estimates of the spectral amplitudes and the covariance matrix. The proposed estimator is numerically shown to provide superior performance as compared to the commonly used least squares Fourier transform (LSFT) estimator.