Controlling spatial correlation in k-space interpolation networks for MRI reconstruction: denoising versus apparent blurring
Purpose: Interpretability is essential for the clinical adoption of state-of-the-art machine learning (ML) methods in magnetic resonance imaging (MRI). Conventional evaluation of ML reconstructions relies heavily on aggregate image metrics that require fully sampled references. These metrics, inherited from classical image processing and natural image ML, often overlook the critical challenge of noise amplification specific to medical image reconstruction. This study aims to analyze the influence of nonlinear activations on spatial noise variance distribution of k-space interpolation networks (RAKI) and to provide a framework for incorporating variance maps during network training. Methods: We present an analytical framework that decomposes pixel-level noise variance into components reflecting linear and nonlinear characteristics of RAKI. By applying automatic differentiation on the image-space equivalent of the network, variance maps are computed during each training iteration, enabling runtime quality assessment beyond data consistency. We introduce apparent blurring, quantifying nonlinear signal mixing without dependence on reference images. By incorporating variance maps into the traning loss as regularizers, our self-informed RAKI architecture (G-factor-informed RAKI, GIF-RAKI) can directly integrate updated noise characteristics during runtime. Results: Experimental results demonstrate that variance components quantitatively explain network behavior. GIF-RAKI outperforms conventional RAKI variants in image fidelity and noise suppression. Conclusion: Our methodology advances practical and theoretical aspects of ML-based MRI reconstruction by reinstating reconstruction noise characterization as a cornerstone for performance evaluation, eliminating the need for fully sampled references. GIF-RAKI also enables optimization of the trade-off between denoising and apparent blurring.