Joint MR-PET Reconstruction Using a Multi-Channel Image Regularizer

Low rank alternating direction method of multipliers reconstruction for MR fingerprinting

PURPOSE

The proposed reconstruction framework addresses the reconstruction accuracy, noise propagation and computation time for magnetic resonance fingerprinting.

METHODS

Based on a singular value decomposition of the signal evolution, magnetic resonance fingerprinting is formulated as a low rank (LR) inverse problem in which one image is reconstructed for each singular value under consideration. This LR approximation of the signal evolution reduces the computational burden by reducing the number of Fourier transformations. Also, the LR approximation improves the conditioning of the problem, which is further improved by extending the LR inverse problem to an augmented Lagrangian that is solved by the alternating direction method of multipliers. The root mean square error and the noise propagation are analyzed in simulations. For verification, in vivo examples are provided.

RESULTS

The proposed LR alternating direction method of multipliers approach shows a reduced root mean square error compared to the original fingerprinting reconstruction, to a LR approximation alone and to an alternating direction method of multipliers approach without a LR approximation. Incorporating sensitivity encoding allows for further artifact reduction.

CONCLUSION

The proposed reconstruction provides robust convergence, reduced computational burden and improved image quality compared to other magnetic resonance fingerprinting reconstruction approaches evaluated in this study. Magn Reson Med 79:83-96, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Advances in PET/MR instrumentation and image reconstruction

The combination of positron emission tomography (PET) and MRI has attracted the attention of researchers in the past approximately 20 years in small-animal imaging and more recently in clinical research. The combination of PET/MRI allows researchers to explore clinical and research questions in a wide number of fields, some of which are briefly mentioned here. An important number of groups have developed different concepts to tackle the problems that PET instrumentation poses to the exposition of electromagnetic fields. We have described most of these research developments in preclinical and clinical experiments, including the few commercial scanners available. From the software perspective, an important number of algorithms have been developed to address the attenuation correction issue and to exploit the possibility that MRI provides for motion correction and quantitative image reconstruction, especially parametric modelling of radiopharmaceutical kinetics. In this work, we give an overview of some exemplar applications of simultaneous PET/MRI, together with technological hardware and software developments.

Simultaneous maximum a posteriori longitudinal PET image reconstruction

Positron emission tomography (PET) is frequently used to monitor functional changes that occur over extended time scales, for example in longitudinal oncology PET protocols that include routine clinical follow-up scans to assess the efficacy of a course of treatment. In these contexts PET datasets are currently reconstructed into images using single-dataset reconstruction methods. Inspired by recently proposed joint PET-MR reconstruction methods, we propose to reconstruct longitudinal datasets simultaneously by using a joint penalty term in order to exploit the high degree of similarity between longitudinal images. We achieved this by penalising voxel-wise differences between pairs of longitudinal PET images in a one-step-late maximum a posteriori (MAP) fashion, resulting in the MAP simultaneous longitudinal reconstruction (SLR) method. The proposed method reduced reconstruction errors and visually improved images relative to standard maximum likelihood expectation-maximisation (ML-EM) in simulated 2D longitudinal brain tumour scans. In reconstructions of split real 3D data with inserted simulated tumours, noise across images reconstructed with MAP-SLR was reduced to levels equivalent to doubling the number of detected counts when using ML-EM. Furthermore, quantification of tumour activities was largely preserved over a variety of longitudinal tumour changes, including changes in size and activity, with larger changes inducing larger biases relative to standard ML-EM reconstructions. Similar improvements were observed for a range of counts levels, demonstrating the robustness of the method when used with a single penalty strength. The results suggest that longitudinal regularisation is a simple but effective method of improving reconstructed PET images without using resolution degrading priors.

Assessment of vectorial total variation penalties on realistic dual-energy CT data

Vectorial extensions of total variation have recently been developed for regularizing the reconstruction and denoising of multi-channel images, such as those arising in spectral computed tomography. Early studies have focused mainly on simulated, piecewise-constant images whose structure may favor total-variation penalties. In the current manuscript, we apply vectorial total variation to real dual-energy CT data of a whole turkey in order to determine if the same benefits can be observed in more complex images with anatomically realistic textures. We consider the total nuclear variation ([Formula: see text]) as well as another vectorial total variation based on the Frobenius norm ([Formula: see text]) and standard channel-by-channel total variation ([Formula: see text]). We performed a series of 3D TV denoising experiments comparing the three TV variants across a wide range of smoothness parameter settings, optimizing each regularizer according to a very-high-dose 'ground truth' image. Consistent with the simulation studies, we find that both vectorial TV variants achieve a lower error than the channel-by-channel TV and are better able to suppress noise while preserving actual image features. In this real data study, the advantages are subtler than in the previous simulation study, although the [Formula: see text] penalty is found to have clear advantages over either [Formula: see text] or [Formula: see text] when comparing material images formed from linear combinations of the denoised energy images.