An esprit-based parameter estimator for spectroscopic data

Abstract

The pulse spin-locking sequence is a common excitation sequence for magnetic resonance and nuclear quadrupole resonance signals, with the resulting measurement data being well modeled as a train of exponentially damped sinusoidals. In this paper, we derive an ESPRIT-based estimator for such signals, together with the corresponding Cramer-Rao lower bound. The proposed estimator is computationally efficient and only requires prior knowledge of the number of spectral lines, which is in general available in the considered applications. Numerical simulations indicate that the proposed method is close to statistically efficient, and that it offers an attractive approach for initialization of existing statistically efficient gradient or search based techniques.<p>QC 20121030</p

A New Frequency Estimation Method for Equally and Unequally Spaced Data

“…In the remainder of the paper, we assume the problem to be normalized so that in (1) is a function defined on the interval Suppose for the moment that we are given sampled values of at the equally spaced nodes on the interval defined by (3) We denote by the vector whose elements are the sampled values , i.e.,…”

“…One important class of spectral estimation problems arises for signals that can be modeled as sums of complex exponentials (or sinusoids) in noise, i.e., for signals that admit the parametric model (1) where is a complex frequency mode with frequency parameter and damping parameter , is a complex amplitude and is an additive noise term. Note that the model (1) includes the case of exponentially damped signals defined by , with important applications notably in spectroscopy (see for instance [2], [3] and references therein). The main goal of frequency estimation is to estimate the values of the parameter vector from a vector of values defined by (1) sampled at positions , where is the number of samples.…”

“…The main goal of frequency estimation is to estimate the values of the parameter vector from a vector of values defined by (1) sampled at positions , where is the number of samples. In the present contribution, the approach to this problem in addition has the capacity to treat the case when is sampled at unequally spaced positions , a frequently appearing situation in many areas, for instance in spectroscopic data analysis [2], [3] and synthetic aperture radar [4], [5]. See also [6] for more examples.…”

An Overview of NQR Signal Detection Algorithms

“…In a typical NQR detection setup, one may first use ET-CAPA to get initial estimates to limit the search space, and then use previously discussed parametric methods to obtain more precise results. An alternative way to form the initial estimates of the expected echo decay and the overall echo-train decay is to use the parametric ET-ESPRIT estimator [28]. This is a computationally and statistically efficient estimator that assumes that the measured signal can be well modeled using (2), and that the additive noise may be approximated as being white, although it has been found that the estimator finds reasonably accurate estimates even in cases when these assumptions are somewhat violated.…”

Non-parametric data-dependent estimation of spectroscopic echo-train signals

“…Typical analysis and detection algorithms for ET data requires some initial estimates of the expected echo decay within each echo, here denoted β, as well as the overall echo train decay, dentoted η, capturing the decay over the various echoes [3,4]. Such estimates are typically obtained using parameteric estimators, such as the ET-ESPRIT and ETAML [3,5], or non-parametric data-adaptive estimators, such as the dCapon, dAPES, or dIAA algorithms [6,7]. The former kind of estimators suffer from requiring a priori knowledge of the precise data structure and model orders, including the presence of any possible interference components, which are commonly oc- curing in all forms of NQR measurements (see e.g., [4]).…”