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 = [g₁; …; 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.