Diffusion-based image super-resolution methods have demonstrated significant advantages over GAN-based approaches, particularly in terms of perceptual quality. Building upon a lengthy Markov chain, diffusion-based methods possess remarkable modeling capacity, enabling them to achieve outstanding performance in real-world scenarios. Unlike previous methods that focus on modifying the noise schedule or sampling process to enhance performance, our approach emphasizes the improved utilization of LR information. We find that different regions of the LR image can be viewed as corresponding to different timesteps in a diffusion process, where flat areas are closer to the target HR distribution but edge and texture regions are farther away. In these flat areas, applying a slight noise is more advantageous for the reconstruction. We associate this characteristic with uncertainty and propose to apply uncertainty estimate to guide region-specific noise level control, a technique we refer to as Uncertainty- guided Noise Weighting. Pixels with lower uncertainty (i.e., flat regions) receive reduced noise to preserve more LR information, therefore improving performance. Furthermore, we modify the network architecture of previous methods to develop our Uncertainty-guided Perturbation Super-Resolution (UPSR) model. Extensive experimental results demonstrate that, despite reduced model size and training overhead, the proposed UPSR method outperforms current state-of-the-art methods across various datasets, both quantitatively and qualitatively.

Deep learning-based bilateral grid processing has emerged as a promising solution for image enhancement, inherently encoding spatial and intensity information while enabling efficient full-resolution processing through slicing operations. However, existing approaches are limited to linear affine transformations, hindering their ability to model complex color relationships. Meanwhile, while multi-layer perceptrons (MLPs) excel at non-linear mappings, traditional MLP-based methods employ globally shared parameters, which is hard to deal with localized variations. To overcome these dual challenges, we propose a Bilateral Grid-based Pixel-Adaptive Multi-layer Perceptron (BPAM) framework. Our approach synergizes the spatial modeling of bilateral grids with the non-linear capabilities of MLPs. Specifically, we generate bilateral grids containing MLP parameters, where each pixel dynamically retrieves its unique transformation parameters and obtain a distinct MLP for color mapping based on spatial coordinates and intensity values. In addition, we propose a novel grid decomposition strategy that categorizes MLP parameters into distinct types stored in separate subgrids. Multi-channel guidance maps are used to extract category-specific parameters from corresponding subgrids, ensuring effective utilization of color information during slicing while guiding precise parameter generation. Extensive experiments on public datasets demonstrate that our method outperforms state-of-the-art methods in performance while maintaining real-time processing capabilities.

Implicit Neural Representations (INRs), as a versatile representation paradigm, have achieved success in various computer vision tasks. Due to the spectral bias of the vanilla multi-layer perceptrons (MLPs), existing methods focus on designing MLPs with sophisticated architectures or repurposing training techniques for highly accurate INRs. In this paper, we delve into the linear dynamics model of MLPs and theoretically identify the empirical Neural Tangent Kernel (eNTK) matrix as a reliable link between spectral bias and training dynamics. Based on this insight, we propose a practical **I**nductive **G**radient **A**djustment (**IGA**) method, which could purposefully improve the spectral bias via inductive generalization of eNTK-based gradient transformation matrix. Theoretical and empirical analyses validate impacts of IGA on spectral bias. Further, we evaluate our method on different INRs tasks with various INR architectures and compare to existing training techniques. The superior and consistent improvements clearly validate the advantage of our IGA. Armed with our gradient adjustment method, better INRs with more enhanced texture details and sharpened edges can be learned from data by tailored impacts on spectral bias. The codes are available at: [https://github.com/LabShuHangGU/IGA-INR](https://github.com/LabShuHangGU/IGA-INR).

Implicit Neural Representation (INR) as a mighty representation paradigm has achieved success in various computer vision tasks recently. Due to the low-frequency bias issue of vanilla multi-layer perceptron (MLP), existing methods have investigated advanced techniques, such as positional encoding and periodic activation function, to improve the accuracy of INR. In this paper, we connect the network training bias with the reparameterization technique and theoretically prove that weight reparameterization could provide us a chance to alleviate the spectral bias of MLP. Based on our theoretical analysis, we propose a Fourier reparameterization method which learns coefficient matrix of fixed Fourier bases to compose the weights of MLP. We evaluate the proposed Fourier reparameterization method on different INR tasks with various MLP architectures, including vanilla MLP, MLP with positional encoding and MLP with advanced activation function, etc. The superiority approximation results on different MLP architectures clearly validate the advantage of our proposed method. Armed with our Fourier reparameterization method, better INR with more textures and less artifacts can be learned from the training data. The codes are available at https://github.com/LabShuHangGU/FR-INR.