Subspace-based parameter estimation of exponentially damped sinusoids using prior knowledge of frequency and phase

Chen, Hua; Huffel, Sabine Van; Boom, A. van den; Bosch, Paul

doi:10.1016/s0165-1684(97)00085-6

Cited by 21 publications

(19 citation statements)

References 5 publications

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“…34 We note that prior knowledge is not always trustworthy in in vivo studies, e.g. the resonance frequency of a metabolite may depend on pH, and additional unknown components may be superimposed on multiplets.…”

Section: In¯uence Of Prior Knowledgementioning

confidence: 98%

Cramér–Rao bounds: an evaluation tool for quantitation

et al. 2001

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The Cramér-Rao lower bounds (CRBs) are the lowest possible standard deviations of all unbiased model parameter estimates obtained from the data. Consequently they give insight into the potential performance of quantitation estimators. Using analytical CRB expressions for spectral parameters of singlets and doublets in noise, one is able to judge the precision as a function of spectral and experimental parameters. We point out the usefulness of these expressions for experimental design. The influence of constraints (chemical prior knowledge) on spectral parameters of the peaks of doublets is demonstrated and the inherent benefits for quantitation are shown.

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Section: In¯uence Of Prior Knowledgementioning

confidence: 98%

Cramér–Rao bounds: an evaluation tool for quantitation

et al. 2001

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“…[8] and the proposed NLLS fit of the filtered signal in Eq. [6] is easily seen if the latter is slightly reformulated. Let…”

Section: Parameter Estimationmentioning

confidence: 98%

“…The minimization in Eq. [6] has been numerically implemented for evaluation by modifying the AMARES algorithm. The new algorithm is referred to as AMARES f in the following and briefly described under Quantification of 1 H Spectra.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…The use of the NLLS fit in Eq. [6] can be motivated by studying the ML estimator for the model in Eq. [1] based on a more general noise assumption.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…It is, however, important to note that the ML interpretation of the filtered NLLS fit in Eq. [6] is valid only if the noise term is Gaussian distributed. This is not the case when a non-Gaussian signal (such as the water signal) is included in the noise term.…”

Section: Parameter Estimationmentioning

confidence: 99%

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