Estimation of parameters of exponentially damped sinusoids using fast maximum likelihood estimation with application to NMR spectroscopy data

We present fast maximum likelihood (FML) estimation of parameters of multiple exponentially damped sinusoids. The FML algorithm was motivated by the desire to analyze data that have many closely spaced components, such as the NMR spectroscopy data of human blood plasma. The computational efficiency of FML lies in reducing the multidimensional search involved in ML estimation into multiple 1-D searches. This is achieved by using our knowledge of the shape of the compressed likelihood function (CLF) in the parameter space. The proposed FML algorithm is an iterative method that decomposes the original data into its constituent signal components and estimates the parameters of the individual components efficiently using our knowledge of the shape of the CLF. The other striking features of the proposed algorithm are that it provides procedures for initialization, has a fast converging iteration stage, and makes use of the information extracted in preliminary iterations to segment the data suitably to increase the effective signal-to-noise ratio (SNR). The computational complexity and the performance of the proposed algorithm are compared with other existing methods such as those based on linear prediction, KiSS/IQML, alternating projections (AP), and expectation-maximization (EM).