  Convolution and deconvolution are essential techniques in various fields,
notably in medical imaging, where they play a crucial role in analyzing dynamic
processes such as blood flow. This paper explores the convolution and
deconvolution of arterial and microvascular signals for determining impulse and
residue functions from in vivo or simulated data and the derivation of the
relationship between the residue function and perfusion metrics such as the
Cerebral Blood Flow (CBF), Mean Transit Time (MTT) and Transit Time to
Heterogeneity (TTH). The paper presents the spectral derivatives as a technique
for recovering the impulse response function from the residue function,
detailing the computational procedures involved and strategies for mitigating
noise effects.
