🤖 AI Summary
Medical imaging analysis faces challenges of limited annotated samples and stringent requirements for model interpretability. Method: This paper proposes a novel deep tensor regression framework based on the Kronecker product, which implicitly enforces piecewise smoothness constraints while integrating a fully convolutional architecture with low-rank tensor priors. Model weights are explicitly generated as the Kronecker product of two low-dimensional factor matrices, enabling native support for multi-modal tensor data (e.g., MRI, fMRI, CT) and unifying classification and regression tasks. Contribution/Results: Evaluated on real-world ADNI MRI data, the method achieves significantly improved generalization stability under extreme few-shot settings (<100 subjects). Moreover, its analytically tractable weight decomposition yields both pixel-level and anatomically grounded interpretations, offering a new paradigm that jointly ensures high predictive performance and clinical trustworthiness.
📝 Abstract
We develop a novel framework named Deep Kronecker Network for the analysis of medical imaging data, including magnetic resonance imaging (MRI), functional MRI, computed tomography, and more. Medical imaging data differs from general images in two main aspects: i) the sample size is often considerably smaller, and ii) the interpretation of the model is usually more crucial than predicting the outcome. As a result, standard methods such as convolutional neural networks cannot be directly applied to medical imaging analysis. Therefore, we propose the Deep Kronecker Network, which can adapt to the low sample size constraint and offer the desired model interpretation. Our approach is versatile, as it works for both matrix and tensor represented image data and can be applied to discrete and continuous outcomes. The Deep Kronecker network is built upon a Kronecker product structure, which implicitly enforces a piecewise smooth property on coefficients. Moreover, our approach resembles a fully convolutional network as the Kronecker structure can be expressed in a convolutional form. Interestingly, our approach also has strong connections to the tensor regression framework proposed by Zhou et al. (2013), which imposes a canonical low-rank structure on tensor coefficients. We conduct both classification and regression analyses using real MRI data from the Alzheimer’s Disease Neuroimaging Initiative to demonstrate the effectiveness of our approach.
