István Homolya

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.