发表机构
Nankai University（南开大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出C$^{2}$-INR，通过方向能量引导的不规则核分配和退火Gumbel-Softmax激活函数选择，实现定制化卷积隐式神经表示，在图像表示、修复和超分辨率任务中超越现有方法。
AI 中文摘要
隐式神经表示（INR）利用神经网络将图像等离散信号表示为连续信号，其中网络权重作为信号本身的紧凑形式。现有大多数INR方法采用多层感知机（MLPs）作为其主干网络。由于这些模型独立渲染每个像素，它们本质上无法利用相邻像素之间存在的空间相关性。相比之下，卷积INR可以并行处理像素，同时固有地考虑像素间依赖关系，使其更适合表示图像。然而，卷积INR仍相对未被充分探索，且大多数依赖固定的架构设置，几乎没有针对特定图像进行适配的空间。在本文中，我们研究卷积INR的网络定制化。我们将传统滤波器替换为不规则的方向核，其分配由图像频谱中的方向能量引导，即能量较强的方向被分配更多数量的核，从而实现内容定制的卷积设置。这些核进一步通过正交基重新表述，以实现更优的稀疏表示。此外，我们引入一种基于退火Gumbel-Softmax的机制用于核级激活函数选择，为每个卷积核提供最合适的激活函数。大量实验表明，我们的方法（即C$^{2}$-INR）在表示、修复和超分辨率等广泛图像处理任务中，在可比较的参数预算下，实现了优于现有最先进方法的性能。
英文摘要
Implicit Neural Representation (INR) leverages neural networks to represent discrete signals such as images as continuous ones, where the network weights serve as a compact form of the signal itself. Most existing INR methods adopt Multi-Layer Perceptrons (MLPs) as their backbone. Since these models render each pixel independently, they inherently fail to exploit the spatial correlations that exist between neighboring pixels. In contrast,convolutional INRs can process pixels in parallel while inherently accounting for inter-pixel dependencies, making them a more natural fit for representing images. Nevertheless, convolutional INRs remain relatively underexplored, and the majority of them rely on fixed architectural settings, leaving little room for image-specific adaptation. In this paper, we investigate network customization for convolutional INRs. We replace conventional filters with irregular directional kernels, whose allocation is guided by the directional energy in the image spectrum, i.e., directions exhibiting stronger energy are assigned a larger number of kernels, enabling content-tailored convolution settings. These kernels are further reformulated via an orthogonal basis to achieve a superior sparse representation. Moreover, we introduce an annealed Gumbel-Softmax-based mechanism for kernel-level activation function selection, which gives the most suitable activation function for each convolution kernel. Extensive experiments demonstrate that our method, namely C$^{2}$-INR, achieves superior performance against state-of-the-art approaches under comparable parameter budgets across a wide range of image processing tasks, including representation, inpainting, and super-resolution.
