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; …; gM] where gm is the measurement vector at gate m. Each gm is a Poisson distributed vector of parameter where P is the projector, W(αm) is the m-th motion of parameter αm, rm is the m-th average random/scatter vector and f is the activity at m = 1. JR is achieved with (1).
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MRI-IR is achieved by solving (2)
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MP-JR is achieved with (3).
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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.