SVD-based Method Research Articles

Determination of in vitro simulated blood cell velocity by Laser-Doppler with state space methods

In this paper a signal processing method based on an important tool of numerical analysis, the singular value decomposition (SVD), is used. This method is applied to the unprocessed output of a Laser-Doppler fluxmeter to obtain parameters that are more sensitive to blood velocity than to hematocrit. The SVD-based method utilizes the exponential shape of the frequency spectrum of the laser light scattered from the moving red blood cells and demonstrates an inverse relationship between the damping constant β associated with the exponential shape and the blood velocity. This method was applied to samples of rat blood of several known hematocrit values that were rotated at different velocities on a turntable. The method extracted one dominant singular value from the spectra, indicating that the spectra can be modeled as a single exponential dominated by scatterings with a single moving red blood cell. A 68% change in inverse velocity resulted in a 50% change in the damping constant (hematocrit 29.5% vol). On the other hand, a 37% change in hematocrit resulted in a far smaller change in the damping constant β of only 17%. Analysis of the extracted parameters shows that the damping constants are far more influenced by blood velocity than by blood hematocrit.

Perturbation analysis of an SVD-based linear prediction method for estimating the frequencies of multiple sinusoids

A linear prediction approach is studied for estimating the frequencies of sinusoids in white noise. It is shown that in the first step, the continuity of the generalized inverse and the concept of angle between subspaces play an important role. The continuity concept helps explain the need for a low rank approximation, and the quality of the approximation is appraised by using the notion of angle between subspaces. For the second step, the sensitivity of the zeros of the predictor polynomial becomes an important consideration and is examined. It is shown that increasing the order of the predictor polynomial and computing the minimum norm solution provides a mechanism to reduce parameter sensitivity. >

Chemical transitions measured by spectra and resolved using singular value decomposition

Shrager, R.I., 1986. Chemical transitions measured by spectra and resolved using singular value decomposition. Chemometrics and Intelligent Laboratory Systems,1: 59–70. A sequence of optical or other spectra, generated by overlapping chemical transitions, may be more easily analyzed after a data reduction step involving singular value decomposition (SVD). The method is described, and its development since 1965 is summarized. Finally, a new SVD-based method described, which corrects some theoretical and practical flaws in past methods.

Modeling of perturbed covariance sequences

An algorithm for obtaining a state-space (Markovian) model of a random process from a finite number of estimated covariance lags is presented and compared to other SVD-based methods. The new algorithm performs well for small data sets in which the estimated covariance sequence is perturbed by estimation errors, and may not even be positive definite. Simulation results are presented for a second-order Markov process.