Abstract:
:Compartmental models are widely used for the mathematical modelling of dynamic studies acquired with positron emission tomography (PET). The numerical problem involves the estimation of a sum of decaying real exponentials convolved with an input function. In exponential spectral analysis (SA), the nonlinear estimation of the exponential functions is replaced by the linear estimation of the coefficients of a predefined set of exponential basis functions. This set-up guarantees fast estimation and attainment of the global optimum. SA, however, is hampered by high sensitivity to noise and, because of the positivity constraints implemented in the algorithm, cannot be extended to reference region modelling. In this paper, SA limitations are addressed by a new rank-shaping (RS) estimator that defines an appropriate regularization over an unconstrained least-squares solution obtained through singular value decomposition of the exponential base. Shrinkage parameters are conditioned on the expected signal-to-noise ratio. Through application to simulated and real datasets, it is shown that RS ameliorates and extends SA properties in the case of the production of functional parametric maps from PET studies.
journal_name
Phys Med Bioljournal_title
Physics in medicine and biologyauthors
Turkheimer FE,Hinz R,Gunn RN,Aston JA,Gunn SR,Cunningham VJdoi
10.1088/0031-9155/48/23/002subject
Has Abstractpub_date
2003-12-07 00:00:00pages
3819-41issue
23eissn
0031-9155issn
1361-6560journal_volume
48pub_type
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