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Using prior knowledge in SVD-based parameter estimation for magnetic resonance spectroscopy--the ATP example
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology, Automatic control. Systems and Control.
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology, Automatic control. Systems and Control.
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology, Automatic control. Systems and Control.
2004 (English)In: IEEE Transactions on Biomedical Engineering, Vol. 51, no 9, 1568-1578 p.Article in journal (Refereed) Published
##### Abstract [en]

We introduce the KNOB-SVD (knowledge based singular

value decomposition)

method for exploiting prior knowledge in MR

spectroscopy based on the singular value decomposition (SVD) of

the data matrix. More specifically we assume that the MR data

is well modeled by the superposition of a given number of exponentially

damped sinusoidal components, and that the dampings $\alpha_k$,

frequencies $\omega_k$ and complex amplitudes $\rho_k$

of some components satisfy the following relations:

$\alpha_k = \alpha$ ($\alpha = \textrm{unknown}$),

$\omega_k = \omega + (k-1) \Delta$ ($\omega = \textrm{unknown}$,

$\Delta = \textrm{known}$), and $\rho_k = c_k \rho$

($\rho = \textrm{unknown}$, $c_k = \textrm{known real constants}$).

The ATP (adenosine triphosphate) complex,

which has one triple peak and two double peaks whose

dampings, frequencies and amplitudes may in some cases be known to

satisfy the above type of relations, is used as a vehicle for describing

our SVD-based method throughout the paper. By means of numerical

examples we show that our method provides more accurate parameter

estimates than a commonly-used general-purpose SVD-based method

and a previously suggested prior knowledge-based SVD method.

##### Place, publisher, year, edition, pages
2004. Vol. 51, no 9, 1568-1578 p.
##### Identifiers
OAI: oai:DiVA.org:uu-70178DiVA: diva2:98089
Available from: 2007-02-08 Created: 2007-02-08 Last updated: 2011-01-12

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http://ieeexplore.ieee.org/iel5/10/29333/01325817.pdf?isnumber=29333&prod=JNL&arnumber=1325817&arSt=+1568&ared=+1578&arAuthor=Stoica%2C+P.%3B+Selen%2C+Y.%3B+Sandgren%2C+N.%3B+Van+Huffel%2C+S.

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Stoica, PeterSelén, YngveSandgren, Niclas
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Department of Information TechnologyAutomatic control