Exploiting multiple shift invariances in multidimensional harmonic retrieval of damped exponentials

We address the problem of estimating the frequencies and damping factors of a multidimensional signal which consists of several damped complex exponentials. Such a problem is of interest in several applications, such as nuclear magnetic resonance spectroscopy, where the 2-dimensional (2D) frequencies and damping factors are used to determine the structure of proteins. We herein propose a new algorithm which exploits the multiple-invariance structure that exists in the data model. Unlike search-based parameter estimation techniques, such as D-MUSIC of Y. Li et al. (1998), which have been developed for multidimensional harmonic retrieval of damped exponentials, our algorithm uses polynomial rooting to obtain the parameters of interest efficiently in a search-free fashion.