Purpose Parallel imaging allows the reconstruction of images from undersampled multi-coil data. The two main approaches are: SENSE, which explicitly uses coil sensitivities, and GRAPPA, which makes use of learned correlations in k-space. The purpose of this work is to clarify their relationship and to develop and evaluate an improved algorithm Theory and Methods A theoretical analysis shows: 1. The correlations in k-space are encoded in the null space of a calibration matrix. 2. Both approaches restrict the solution to a subspace spanned by the sensitivities. 3. The sensitivities appear as the main eigenvector of a reconstruction operator computed from the null space. The basic assumptions and the quality of the sensitivity maps are evaluated in experimental examples. The appearance of additional eigenvectors motivates an extended SENSE reconstruction with multiple maps, which is compared to existing methods Results The existence of a null space and the high quality of the extracted sensitivities are confirmed. The extended reconstruction combines all advantages of SENSE with robustness to certain errors similar to GRAPPA. Conclusion In this paper the gap between both approaches is finally bridged. A new autocalibration technique combines the benefits of both.

The task of MRI fingerprinting is to identify tissue parameters from complex-valued MRI signals. The prevalent approach is dictionary based, where a test MRI signal is compared to stored MRI signals with known tissue parameters and the most similar signals and tissue parameters retrieved. Such an approach does not scale with the number of parameters and is rather slow when the tissue parameter space is large.Our first novel contribution is to use deep learning as an efficient nonlinear inverse mapping approach. We generate synthetic (tissue, MRI) data from an MRI simulator, and use them to train a deep net to map the MRI signal to the tissue parameters directly. Our second novel contribution is to develop a complex-valued neural network with new cardioid activation functions. Our results demonstrate that complex-valued neural nets could be much more accurate than real-valued neural nets at complex-valued MRI fingerprinting.

The results of this study allow for the quantitative evaluation of in vivo human physes in future studies and development of predictive models for limb length discrepancy.

In Fourier-based medical imaging, sampling below the Nyquist rate results in an underdetermined system, in which a linear reconstruction will exhibit artifacts. Another consequence is lower signal-to-noise ratio (SNR) because of fewer acquired measurements. Even if one could obtain information to perfectly disambiguate the underdetermined system, the reconstructed image could still have lower image quality than a corresponding fully sampled acquisition because of reduced measurement time. The coupled effects of low SNR and underdetermined system during reconstruction makes it difficult to isolate the impact of low SNR on image quality. To this end, we present an image quality prediction process that reconstructs fully sampled, fully determined data with noise added to simulate the SNR loss induced by a given undersampling pattern. The resulting prediction image empirically shows the effects of noise in undersampled image reconstruction without any effect from an underdetermined system. We discuss how our image quality prediction process simulates the distribution of noise for a given undersampling pattern, including variable density sampling that produces colored noise in the measurement data. An interesting consequence of our prediction model is that recovery from an underdetermined nonuniform sampling is equivalent to a weighted least squares optimization that accounts for heterogeneous noise levels across measurements. Through experiments with synthetic and in vivo datasets, we demonstrate the efficacy of the image quality prediction process and show that it provides a better estimation of reconstruction image quality than the corresponding fully sampled reference image.