ArticleMagnetic resonance in medicine2025
Image space formalism of convolutional neural networks for k-space interpolation.
Article in Magnetic resonance in medicine, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Image-Based Assessment of External Quality Traits in Chinese Bayberry (Foods (Basel, Switzerland) · 2026Article
- Adaptation of an arterial spin labeling sequence for the assessment of brain perfusion on a 0.35 T MR-Linac.Magma (New York, N.Y.) · 2026Article
- Image space formalism of convolutional neural networks for k-space interpolation.Magnetic resonance in medicine · 2025Article
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7 authors.
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Abstract
purposeNoise 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. THEORY AND
methodsThe 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; 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.
resultsThe 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.
conclusionThe image space formalism of RAKI provides the means for analytical quantitative noise-propagation analysis and human-readable visualization of the effects of the nonlinear activation functions in k-space.
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