TABLE I.

Glossary of symbols

VOI	Volume of interest in the brain tissue
Ca	Contrast concentration at the arterial inlet of a VOI
Cv	Contrast concentration at the venous outlet of the VOI
Ctis	Contrast concentration in the brain tissue
$m_{\text{voi}}^{\text{c}}\left(t\right)$	Mass of contrast in the VOI at time t
$m_{\text{in}}^{\text{c}}\left(t\right)$	Mass of contrast passing though arterial inlet by t
$m_{\text{out}}^{\text{c}}\left(t\right)$	Mass of contrast drained though venous outlet by t
F	Volume of blood passing through the VOI per unit time
$V_{\text{voi }}^{\text{tis }}$	Volume of brain tissue in the VOI
ρ	Mass density of brain tissue
H	Ratio between arterial and capillary hematocrits
h(t)	Probability density function of blood transit time
r(t)	Residue function
k(t)	Flow-scaled residue function
x	Spatial location in the brain
xa	Spatial location of a major feeding artery
$\mathcal{I}\left(x,t\right)$	True pixel value of CTP source image
I(x,t)	Pixel value of the measured source image
Ib(x)	Pixel value of the measured baseline image
I′ (x, t)	Baseline-corrected image: I′ (x, t) = I(x, t) − Ib(x)
c	Measured tissue enhancement curve, vectorized
$\overline{c}$	Expected form of c
c0	Truth of the tissue enhancement curve
biasc	$\overline{c}-c_0$
A	Arterial enhancement convolution matrix
σ1	The largest singular value of A
λ	Weight of regularizer used in deconvolution
λrel	Relative weighting factor: λ = λrelσ1
k*	Estimated flow-scaled residue function
C	Autocovariance matrix of a temporal curve
N	Total number of postbaseline time frames
Nb	Total number of baseline time frames
${\sigma }_0^2$	Noise variance of CTP source images
${\sigma }_{\text{b}}^2$	Noise variance of the baseline image
max	Peak value of a dynamic curve
tmax	Time to peak of the residue function
⊤	Transpose of a matrix or vector
Δt	Time interval between two consecutive source frames
E	The identity matrix
J	The all-one matrix