Generalised Q-Sampling Imaging#

These notes are to help the user of the DIPY module understand Frank Yeh’s Generalised Q-Sampling Imaging (GQI) [reference?].

The starting point is the classical formulation of joint k-space and q-space imaging (Calaghan 8.3.1 p. 438) using the narrow pulse gradient spin echo (PGSE) sequence of Tanner and Stejskal:

S(k,q)=ρ(r)exp[j2πkr]PΔ(r|r,Δ)exp[j2πq(rr)]drdr.

Here S is the (complex) RF signal measured at spatial wave number k and magnetic gradient wave number q.

ρ is the local spin density (number of protons per unit volume contributing to the RF signal).

Δ is the diffusion time scale of the sequence.

PΔ is the averages diffusion propagator (transition probability distribution).