Abstract
In recent years, implicit neural representations(INRs) have gained popularity in the computer vision community. This is mainly due to the strong performance of INRs in many computer vision tasks. These networks can extract a continuous signal representation given a discrete signal representation. In previous studies, it has been repeatedly shown that INR performance has a strong correlation with the activation functions used in its multilayer perceptrons. Although numerous activation functions have been proposed that are competitive with one another, they share some common set of challenges such as spectral bias(Lack of sensitivity to high-frequency content in signals), limited robustness to signal noise and difficulties in simultaneous capturing both local and global features. and furthermore, the requirement for manual parameter tuning. To address these issues, we introduce a novel activation function, Band Shifted Raised Cosine Activated Implicit Neural Networks \textbf{(BandRC)} tailored to enhance signal representation capacity further. We also incorporate deep prior knowledge extracted from the signal to adjust the activation functions through a task-specific model. Through a mathematical analysis and a series of experiments which include image reconstruction (with a +8.93 dB PSNR improvement over the nearest counterpart), denoising (with a +0.46 dB increase in PSNR), super-resolution (with a +1.03 dB improvement over the nearest State-Of-The-Art (SOTA) method for 6X super-resolution), inpainting, and 3D shape reconstruction we demonstrate the dominance of BandRC over existing state of the art activation functions.
Abstract (translated)
近年来，隐式神经表示（INRs）在计算机视觉社区中获得了很大的关注。这主要是由于它们在许多计算机视觉任务中的强大性能表现。这些网络能够从离散信号表示中提取出连续的信号表示。以往的研究反复表明，多层感知器中使用的激活函数对INR的性能有很强的相关性。尽管提出了众多相互竞争的激活函数，但它们都面临一些共同挑战：如谱偏差（信号高频内容缺乏敏感度）、对抗信号噪声的能力有限以及难以同时捕捉局部和全局特征等问题，并且还需要手动调整参数。 为了应对这些挑战，我们引入了一种新型激活函数——频带偏移提升余弦激活隐式神经网络（BandRC），旨在进一步增强信号表示能力。此外，我们还整合了从信号中提取的深度先验知识，通过特定任务模型来调整激活函数。通过对数学分析和一系列实验进行验证（包括图像重建、去噪、超分辨率处理以及3D形状重构等场景），结果显示BandRC在现有最先进的激活函数性能上占据主导地位：图像重建提高了8.93 dB PSNR；去噪提升了0.46 dB PSNR，超分辨率处理中对于6倍放大任务，相比最近的最先进方法（SOTA）改进了1.03 dB。
URL
https://arxiv.org/abs/2505.11640
