Enhanced resolution based on minimum variance estimation and exponential data modeling

Abstract In various signal processing applications, it is desired to appropriately modify a given data set so that the modified data set possesses prescribed properties. The modification of the given data set serves as a preprocessing step of ‘cleaning up’ the data before estimating the values of the signal parameters. In this paper, evaluation and improvement of a signal enhancement algorithm, originally proposed by Tufts, Kumaresan and Kirsteins and recently generalized by Cadzow, are presented. In essence, the newly proposed algorithm first arranges the data in a very rectangular (instead of a square) Hankel structured matrix in order to make the corresponding signal-only data matrix orthogonal to the noise, then computes a minimum variance (instead of a least squares) estimate of the signal-only data matrix and finally restores the Hankel structure of the computed minimum variance estimate. An extensive set of simulations is given demonstrating a significant improvement in resolution performance over Cadzow's method at a comparable parameter accuracy. Moreover, arranging the data in a very rectangular matrix reduces drastically the required computation time. In particular, the newly proposed signal enhancement algorithm can be successfully applied to the quantitative time-domain analysis of Nuclear Magnetic Resonance (NMR) data.

[1]  Sabine Van Huffel,et al.  Total least squares problem - computational aspects and analysis , 1991, Frontiers in applied mathematics.

[2]  D. van Ormondt,et al.  Analysis of NMR Data Using Time Domain Fitting Procedures , 1992 .

[3]  Tapan K. Sarkar,et al.  Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise , 1990, IEEE Trans. Acoust. Speech Signal Process..

[4]  D. van Ormondt,et al.  Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals , 1987 .

[5]  B. De Moor,et al.  The fit of a sum of exponentials to noisy data , 1987 .

[6]  Fu Li,et al.  Unified performance analysis of subspace-based estimation algorithms , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[7]  Björn E. Ottersten,et al.  Sensor array processing based on subspace fitting , 1991, IEEE Trans. Signal Process..

[8]  James A. Cadzow,et al.  Signal enhancement-a composite property mapping algorithm , 1988, IEEE Trans. Acoust. Speech Signal Process..

[9]  R. Kumaresan,et al.  Data adaptive signal estimation by singular value decomposition of a data matrix , 1982, Proceedings of the IEEE.

[10]  Sabine Van Huffel,et al.  Comparison of total least squares and instrumental variable methods for parameter estimation of transfer function models , 1989 .

[11]  S. Van Huffel,et al.  IMPROVED QUANTITATIVE TIME-DOMAIN ANALYSIS OF NMR DATA BY TOTAL LEAST SQUARES. , 1991 .

[12]  R. Kumaresan,et al.  Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noise , 1982 .

[13]  K. Arun,et al.  State-space and singular-value decomposition-based approximation methods for the harmonic retrieval problem , 1983 .

[14]  Bart De Moor,et al.  The singular value decomposition and long and short spaces of noisy matrices , 1993, IEEE Trans. Signal Process..

[15]  Gene H. Golub,et al.  Matrix computations , 1983 .

[16]  Donald W. Tufts,et al.  Estimation of a signal waveform from noisy data using low-rank approximation to a data matrix , 1993, IEEE Trans. Signal Process..