A singular value decomposition based algorithm for multicomponent exponential fitting of NMR relaxation signals

This work concerns singular value decomposition (SVD) and state space based analysis of a nuclear magnetic resonance relaxation signal. The new method yields a significant improvement over conventional methods. Given a set of noisy data {y0, y1,…, ym} measured at equidistant points on the time axis, find n (n < 12m) exponents bi and coefficients ci such that y(t) = ∑ici exp(bit) yields a good data approximation. An important result of the method is the possibility of detecting the number of exponentials present in a signal (e.g. NMR free induction decay) by examining the values given in the singular value matrix. A software implementation of the method was done and the program was tested both with simulated and real NMR relaxation signals.