Computationally Efficient Estimation of Multi-dimensional Damped Modes using Sparse Wideband Dictionaries

Estimating the parameters of non-uniformly sampled multi-dimensional damped modes is computationally cumbersome, especially if the model order of the signal is not assumed to be known a priori. In this work, we examine the possibility of using the recently introduced wideband dictionary framework to formulate a computationally efficient estimator that iteratively refines the estimates of the candidate frequency and damping coefficients for each component. The proposed wideband dictionary allows for the use of a coarse initial grid without increasing the risk of not identifying closely spaced components, resulting in a substantial reduction in computational complexity. The performance of the proposed method is illustrated using both simulated and real spectroscopy data, clearly showing the improved performance as compared to previous techniques.