In this work we adapt a method to manipulate magnetic
resonance data such that the moments of the signal spatial
distribution are readily accessible. Using analysis of the complex
nuclear magnetic resonance (NMR) signal in the vicinity of the centre
of k-space (reciprocal image space) we access the first three
moments of the signal spatial distribution. This approach is analogous
to that developed to probe the moments of displacement
probability distributions (propagators) via analysis of q-space
[1,2]. It is motivated by specific applications where signal-to-noise
ratio (SNR) is critical (e.g. mobile low magnetic field NMR spectrometers)
but where rapid acquisition is also desirable. Whilst
rapid MRI techniques (e.g. FLASH [3], RARE [4] and EPI [5]) offer
total acquisition times on the order of tens to hundreds of milliseconds
to fully sample k-space, there is in practice a trade-off
between the magnetic resonance imaging (MRI) signal intensity
and imaging speed. This becomes prohibitive at low-magnetic
fields as SNR / B0
1.75 [1] where B0 is the static magnetic field
strength employed. More conventional MRI pulse sequences (e.g.
spin echo imaging) have total acquisition times of the order of minutes
to typically sample all of k-space at sufficient SNR. To improve