Parallel imaging with linear predictability takes advantage of information present in multiple receive coils to accurately reconstruct the image with fewer samples. Commonly used algorithms based on linear predictability include GRAPPA and SPIRiT. We present a sufficient condition for reconstruction based on the direction of undersampling and the arrangement of the sensing coils. This condition is justified theoretically and examples are shown using real data. We also propose a metric based on the fully-sampled auto-calibration region which can show which direction(s) of undersampling will allow for a good quality image reconstruction.
In this paper, we review physics- and data-driven reconstruction techniques for simultaneous positron emission tomography (PET) / magnetic resonance imaging (MRI) systems, which have significant advantages for clinical imaging of cancer, neurological disorders, and heart disease. These reconstruction approaches utilize priors, either structural or statistical, together with a physics-based description of the PET system response. However, due to the nested representation of the forward problem, direct PET/MRI reconstruction is a nonlinear problem. We elucidate how a multi-faceted approach accommodates hybrid data- and physics-driven machine learning for reconstruction of 3D PET/MRI, summarizing important deep learning developments made in the last 5 years to address attenuation correction, scattering, low photon counts, and data consistency. We also describe how applications of these multi-modality approaches extend beyond PET/MRI to improving accuracy in radiation therapy planning. We conclude by discussing opportunities for extending the current state-of-the-art following the latest trends in physics- and deep learning-based computational imaging and next-generation detector hardware.
The Gridding algorithm has shown great utility for reconstructing images from non-uniformly spaced samples in the Fourier domain in several imaging modalities. Due to the non-uniform spacing, some correction for the variable density of the samples must be made. Existing methods for generating density compensation values are either sub-optimal or only consider a finite set of points (a set of measure 0) in the optimization. This manuscript presents the first density compensation algorithm for a general trajectory that takes into account the point spread function over a set of non-zero measure. We show that the images reconstructed with Gridding using the density compensation values of this method are of superior quality when compared to density compensation weights determined in other ways. Results are shown with a numerical phantom and with magnetic resonance images of the abdomen and the knee.