方向性全变分正则化隐式神经表示（DTV-INR）用于退化成像域中的连续超分辨率
Directional Total Variation-Regularized Implicit Neural Representations (DTV-INR) for Continuous Super-Resolution in Degraded Imaging Domains
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中文总结 AI 辅助
提出DTV-INR，结合隐式神经网络与方向性全变分正则化，实现退化图像连续超分辨率，显著提升PSNR并抑制阶梯伪影。
中文摘要 AI 辅助
本文提出方向性全变分正则化隐式神经表示（DTV-INR），这是一种先进的变分范式，将坐标驱动的隐式神经网络与各向异性、基于结构张量的全变分正则化器协同集成，专用于分辨率无关的图像超分辨率。将连续到离散的采集过程建模为不适定逆问题框架，我们的公式为SIREN架构的坐标网络配备动态黎曼度量张量场D(x)。通过利用其谱分解，所提出的正则化器优先将扩散引导至主导结构轮廓方向，同时惩罚跨边缘耗散，成功规避了标量全变分方案固有的阶梯伪影。我们严格证明了该公式在H^1(Omega)中的适定性，通过建立变分极小元的存在性、唯一性和度量稳定性，并通过交替投影优化算法实现，该算法将网络参数调整与自适应张量场更新解耦。在临床脑磁共振成像（MRI）和生物医学透射电子显微镜上进行的全面实验证实了显著的定量和定性改进，在连续（非整数）上采样因子下，PSNR相对于基线无正则化INR提升达+5.05 dB，相对于各向同性TV-INR提升+1.71-2.85 dB，同时具有高达sigma_eta = 0.10的显著噪声鲁棒性和单调预条件收敛行为。
英文摘要
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.
发表机构
- Islamic Azad University（伊斯兰阿扎德大学）
机构由 AI 辅助整理，请以论文原文为准。
