4-D PET joint image reconstruction/non-rigid motion estimation with limited MRI prior information

Motion compensated gated PET image reconstruction methods include joint-reconstruction (JR) and indirect reconstruction (IR) with pre-estimated motion from MRI (MRI-IR). JR suffers from poor PET data quality whereas MRI-IR requires high-quality MRI volumes at each gate. We propose a penalised maximum-likelihood approach combining JR and MRI-IR. Our method is referred to as minimal MRI prior JR (MP-JR).

The M gates data are stored in g = [g ₁; …; g _M ] where g _m is the measurement vector at gate m. Each g _m is a Poisson distributed vector of parameter where P is the projector, W(α _m ) is the m-th motion of parameter α _m , r _m is the m-th average random/scatter vector and f is the activity at m = 1. JR is achieved with (1).

(1)

MRI-IR is achieved by solving (2)

(2)

MP-JR is achieved with (3).

(3)

The first term accounts for PET data, whereas the second term accounts for MRI motion information from subset S. The last term controls temporal smoothness.

We tested each method on 9 PET FDG volumes generated from a real dynamic MRI sequence. Tumours were added to the activity distribution (invisible in the MRI). The gates subset S for MP-JR contains the reference gate, end-inspiration and end-expiration. Reconstruction profiles 1 show that MRI-IR improves edges visible in the MRI but degrades the tumours. On the contrary, JR performs well on tumours, but the edges are poorly reconstructed. MP-JR appears to perform well on both organ edges and tumours.

Figure 1

Reconstruction profiles: (a) across tumours; (b) across liver.

MP-JR seems to perform well where both JR and MRI-IR under-perform. This is due to the fact that MP-JR relies on both MRI and PET data. In addition, results tend to show that with temporal smoothing on B-spline parameters, a subset of MRI volumes provides sufficient information.