Bézier Curve Deconvolution for Model-Free Quantification of Cerebral Perfusion
André Ahlgren1, Ronnie Wirestam1, Freddy Ståhlberg1,2,3, and Linda Knutsson1
1Department of Medical Radiation Physics, Lund University, Lund, Sweden, 2Department of Diagnostic Radiology, Lund University, Lund, Sweden, 3Lund University Bioimaging Center, Lund University, Lund, Sweden
Deconvolution is an
ill-posed and ill-conditioned inverse problem that often yields non-physiological residue functions in perfusion MRI. Deconvolution methods
based on Fourier transform or matrix decomposition often yield solutions with spurious
oscillations. Although the perfusion value, estimated from the peak of the
tissue impulse response function, may still be useful, any estimate that
depends on the actual shape of the residue function will be prone to errors. To
obtain physiologically reasonable residue functions in perfusion MRI, we
propose the use of Bézier curves, and demonstrate initial experiences from the
application to DSC-MRI in vivo data.
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