Peter M. Jakob

Peter Dawood, Martin Blaimer, Jürgen Herrler et al.

Purpose: To non-heuristically identify dedicated variable flip angle (VFA) schemes optimized for the point-spread function (PSF) and signal-to-noise ratio (SNR) of multiple tissues in 3D FSE sequences with very long echo trains at 7T. Methods: The proposed optimization considers predefined SAR constraints and target contrast using an end-to-end learning framework. The cost function integrates components for contrast fidelity (SNR) and a penalty term to minimize image blurring (PSF) for multiple tissues. By adjusting the weights of PSF/SNR cost-function components, PSF- and SNR-optimized VFAs were derived and tested in vivo using both the open-source Pulseq standard on two volunteers as well as vendor protocols on a 7T MRI system with parallel transmit extension on three volunteers. Results: PSF-optimized VFAs resulted in significantly reduced image blurring compared to standard VFAs for T2w while maintaining contrast fidelity. Small white and gray matter structures, as well as blood vessels, are more visible with PSF-optimized VFAs. Quantitative analysis shows that the optimized VFA yields 50% less deviation from a sinc-like reference PSF than the standard VFA. The SNR-optimized VFAs yielded images with significantly improved SNR in a white and gray matter region relative to standard (81.2\pm18.4 vs. 41.2\pm11.5, respectively) as trade-off for elevated image blurring. Conclusion: This study demonstrates the potential of end-to-end learning frameworks to optimize VFA schemes in very long echo trains for 3D FSE acquisition at 7T in terms of PSF and SNR. It paves the way for fast and flexible adjustment of the trade-off between PSF and SNR for 3D FSE.

Peter Dawood, Felix Breuer, Istvan Homolya et al.

Purpose: Noise resilience in image reconstructions by scan-specific robust artificial neural networks for k-space interpolation (RAKI) is linked to nonlinear activations in k-space. To gain a deeper understanding of this relationship, an image space formalism of RAKI is introduced for analyzing noise propagation analytically, identifying and characterizing image reconstruction features and to describe the role of nonlinear activations in a human readable manner. Methods: The image space formalism for RAKI inference is employed by expressing nonlinear activations in k-space as element-wise multiplications with activation masks, which transform into convolutions in image space. Jacobians of the de-aliased, coil-combined image relative to the aliased coil images can be expressed algebraically, and thus, the noise amplification is quantified analytically (g-factor maps). We analyze the role of nonlinearity for noise resilience by controlling the degree of nonlinearity in the reconstruction model via the negative slope parameter in leaky ReLU. Results: The analytical g-factor maps correspond with those obtained from Monte Carlo simulations and from an auto differentiation approach for in vivo brain images. Apparent blurring and contrast loss artifacts are identified as implications of enhanced noise resilience. These residual artifacts can be traded against noise resilience by adjusting the degree of nonlinearity in the model (Tikhonov-like regularization) in case of limited training data. The inspection of image space activations reveals an autocorrelation pattern leading to a potential center artifact. Conclusion: The image space formalism of RAKI provides the means for analytical quantitative noisepropagation analysis and human-readable visualization of the effects of the nonlinear activation functions in k-space.

Peter Dawood, Felix Breuer, Paul R. Burd et al.

Purpose: To evaluate an iterative learning approach for enhanced performance of Robust Artificial-neural-networks for K-space Interpolation (RAKI), when only a limited amount of training data (auto-calibration signals, ACS) are available for accelerated standard 2D imaging. Methods: In a first step, the RAKI model was optimized for the case of strongly limited training data amount. In the iterative learning approach (termed iterative RAKI), the optimized RAKI model is initially trained using original and augmented ACS obtained from a linear parallel imaging reconstruction. Subsequently, the RAKI convolution filters are refined iteratively using original and augmented ACS extracted from the previous RAKI reconstruction. Evaluation was carried out on 200 retrospectively undersampled in-vivo datasets from the fastMRI neuro database with different contrast settings. Results: For limited training data (18 and 22 ACS lines for R=4 and R=5, respectively), iterative RAKI outperforms standard RAKI by reducing residual artefacts and yields strong noise suppression when compared to standard parallel imaging, underlined by quantitative reconstruction quality metrics. In combination with a phase constraint, further reconstruction improvements can be achieved. Additionally, iterative RAKI shows better performance than both GRAPPA and RAKI in case of pre-scan calibration with varying contrast between training- and undersampled data. Conclusion: The iterative learning approach with RAKI benefits from standard RAKIs well known noise suppression feature but requires less original training data for the accurate reconstruction of standard 2D images thereby improving net acceleration.