Summary
Super-resolution means making images clearer and more detailed when you enlarge them, which is especially hard when images are noisy or blurry. The authors introduce a new mathematical method that helps neural networks focus on important image edges and directions to better enhance resolution without common blurring or distortion artifacts. They tested their approach on medical brain scans and electron microscope images, showing significant improvement in image quality and better resistance to noise compared to previous methods. This method works for any enlargement scale, even non-integer factors, making it versatile for various imaging tasks.
What this means in practice
- •For medical imaging teams: Enhance resolution of brain MRI scans for clearer clinical diagnosis without introducing common image artifacts.
- •For microscopy imaging engineers: Improve detail and noise resistance in transmission electron microscopy images for better structural analysis.
Abstract
In this paper, we introduce the Directional Total Variation-Regularized Implicit Neural Representation (DTV-INR), an advanced variational paradigm that synergistically integrates coordinate-driven implicit neural networks with an anisotropic, structure-tensor-informed total variation regularizer tailored for resolution-agnostic image super-resolution. Casting the continuous-to-discrete acquisition process into an ill-posed inverse problem framework, our formulation equips a SIREN-architected coordinate network with a dynamic Riemannian metric tensor field D(x). By leveraging its spectral decomposition, the proposed regularizer preferentially directs diffusion parallel to dominant structural contours while penalizing cross-edge dissipation, successfully circumventing the classical staircasing artifacts inherent to scalar total variation schemes. We rigorously prove the well-posedness of this formulation in H^1(Omega) by establishing the existence, uniqueness, and metric stability of the variational minimizer, and realize this via an alternating projected optimization algorithm that decouples network parameter tuning from adaptive tensor field updates. Comprehensive experiments conducted on clinical brain magnetic resonance imaging (MRI) and biomedical transmission electron microscopy confirm substantial quantitative and qualitative improvements, yielding PSNR enhancements reaching +5.05 dB over baseline unregularized INRs and +1.71-2.85 dB over isotropic TV-INR across continuous (non-integer) upsampling factors, alongside remarkable noise robustness up to sigma_eta = 0.10 and monotonic preconditioned convergence behavior.