Super-resolving Real-world Image Illumination Enhancement: A New Dataset and A Conditional Diffusion Model

Most existing super-resolution methods and datasets have been developed to improve the image quality in well-lighted conditions. However, these methods do not work well in real-world low-light conditions as the images captured in such conditions lose most important information and contain significant unknown noises. To solve this problem, we propose a SRRIIE dataset with an efficient conditional diffusion probabilistic models-based method. The proposed dataset contains 4800 paired low-high quality images. To ensure that the dataset are able to model the real-world image degradation in low-illumination environments, we capture images using an ILDC camera and an optical zoom lens with exposure levels ranging from -6 EV to 0 EV and ISO levels ranging from 50 to 12800. We comprehensively evaluate with various reconstruction and perceptual metrics and demonstrate the practicabilities of the SRRIIE dataset for deep learning-based methods. We show that most existing methods are less effective in preserving the structures and sharpness of restored images from complicated noises. To overcome this problem, we revise the condition for Raw sensor data and propose a novel time-melding condition for diffusion probabilistic model. Comprehensive quantitative and qualitative experimental results on the real-world benchmark datasets demonstrate the feasibility and effectivenesses of the proposed conditional diffusion probabilistic model on Raw sensor data. Code and dataset will be available at https://github.com/Yaofang-Liu/Super-Resolving

Redefining Temporal Modeling in Video Diffusion: The Vectorized Timestep Approach

Diffusion models have revolutionized image generation, and their extension to video generation has shown promise. However, current video diffusion models~(VDMs) rely on a scalar timestep variable applied at the clip level, which limits their ability to model complex temporal dependencies needed for various tasks like image-to-video generation. To address this limitation, we propose a frame-aware video diffusion model~(FVDM), which introduces a novel vectorized timestep variable~(VTV). Unlike conventional VDMs, our approach allows each frame to follow an independent noise schedule, enhancing the model's capacity to capture fine-grained temporal dependencies. FVDM's flexibility is demonstrated across multiple tasks, including standard video generation, image-to-video generation, video interpolation, and long video synthesis. Through a diverse set of VTV configurations, we achieve superior quality in generated videos, overcoming challenges such as catastrophic forgetting during fine-tuning and limited generalizability in zero-shot methods.Our empirical evaluations show that FVDM outperforms state-of-the-art methods in video generation quality, while also excelling in extended tasks. By addressing fundamental shortcomings in existing VDMs, FVDM sets a new paradigm in video synthesis, offering a robust framework with significant implications for generative modeling and multimedia applications.

Quaternion Nuclear Norm minus Frobenius Norm Minimization for color image reconstruction

Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and artifacts in the reconstructed image. To address this, we present Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF), a novel approach for color image reconstruction. QNMF utilizes quaternion algebra to capture the relationships among RGB channels comprehensively. By employing a regularization technique that involves nuclear norm minus Frobenius norm, QNMF approximates the underlying low-rank structure of quaternion-encoded color images. Theoretical proofs are provided to ensure the method's mathematical integrity. Demonstrating versatility and efficacy, the QNMF regularizer excels in various color low-level vision tasks, including denoising, deblurring, inpainting, and random impulse noise removal, achieving state-of-the-art results.

Hyper-Compression: Model Compression via Hyperfunction

The rapid growth of large models' size has far outpaced that of GPU memory. To bridge this gap, inspired by the succinct relationship between genotype and phenotype, we turn the model compression problem into the issue of parameter representation to propose the so-called hyper-compression. The hyper-compression uses a hyperfunction to represent the parameters of the target network, and notably, here the hyperfunction is designed per ergodic theory that relates to a problem: if a low-dimensional dynamic system can fill the high-dimensional space eventually. Empirically, the proposed hyper-compression enjoys the following merits: 1) \textbf{P}referable compression ratio; 2) \textbf{N}o post-hoc retraining; 3) \textbf{A}ffordable inference time; and 4) \textbf{S}hort compression time. It compresses LLaMA2-7B in an hour and achieves close-to-int4-quantization performance, without retraining and with a performance drop of less than 1\%. Our work has the potential to invigorate the field of model compression, towards a harmony between the scaling law and the stagnation of hardware upgradation.

Deep Inertia $L_p$ Half-Quadratic Splitting Unrolling Network for Sparse View CT Reconstruction

Sparse view computed tomography (CT) reconstruction poses a challenging ill-posed inverse problem, necessitating effective regularization techniques. In this letter, we employ $L_p$-norm ($0<p<1$) regularization to induce sparsity and introduce inertial steps, leading to the development of the inertial $L_p$-norm half-quadratic splitting algorithm. We rigorously prove the convergence of this algorithm. Furthermore, we leverage deep learning to initialize the conjugate gradient method, resulting in a deep unrolling network with theoretical guarantees. Our extensive numerical experiments demonstrate that our proposed algorithm surpasses existing methods, particularly excelling in fewer scanned views and complex noise conditions.

Don't Fear Peculiar Activation Functions: EUAF and Beyond

In this paper, we propose a new super-expressive activation function called the Parametric Elementary Universal Activation Function (PEUAF). We demonstrate the effectiveness of PEUAF through systematic and comprehensive experiments on various industrial and image datasets, including CIFAR10, Tiny-ImageNet, and ImageNet. Moreover, we significantly generalize the family of super-expressive activation functions, whose existence has been demonstrated in several recent works by showing that any continuous function can be approximated to any desired accuracy by a fixed-size network with a specific super-expressive activation function. Specifically, our work addresses two major bottlenecks in impeding the development of super-expressive activation functions: the limited identification of super-expressive functions, which raises doubts about their broad applicability, and their often peculiar forms, which lead to skepticism regarding their scalability and practicality in real-world applications.

No One-Size-Fits-All Neurons: Task-based Neurons for Artificial Neural Networks

Biologically, the brain does not rely on a single type of neuron that universally functions in all aspects. Instead, it acts as a sophisticated designer of task-based neurons. In this study, we address the following question: since the human brain is a task-based neuron user, can the artificial network design go from the task-based architecture design to the task-based neuron design? Since methodologically there are no one-size-fits-all neurons, given the same structure, task-based neurons can enhance the feature representation ability relative to the existing universal neurons due to the intrinsic inductive bias for the task. Specifically, we propose a two-step framework for prototyping task-based neurons. First, symbolic regression is used to identify optimal formulas that fit input data by utilizing base functions such as logarithmic, trigonometric, and exponential functions. We introduce vectorized symbolic regression that stacks all variables in a vector and regularizes each input variable to perform the same computation, which can expedite the regression speed, facilitate parallel computation, and avoid overfitting. Second, we parameterize the acquired elementary formula to make parameters learnable, which serves as the aggregation function of the neuron. The activation functions such as ReLU and the sigmoidal functions remain the same because they have proven to be good. Empirically, experimental results on synthetic data, classic benchmarks, and real-world applications show that the proposed task-based neuron design is not only feasible but also delivers competitive performance over other state-of-the-art models.

Kernel Correlation-Dissimilarity for Multiple Kernel k-Means Clustering

The main objective of the Multiple Kernel k-Means (MKKM) algorithm is to extract non-linear information and achieve optimal clustering by optimizing base kernel matrices. Current methods enhance information diversity and reduce redundancy by exploiting interdependencies among multiple kernels based on correlations or dissimilarities. Nevertheless, relying solely on a single metric, such as correlation or dissimilarity, to define kernel relationships introduces bias and incomplete characterization. Consequently, this limitation hinders efficient information extraction, ultimately compromising clustering performance. To tackle this challenge, we introduce a novel method that systematically integrates both kernel correlation and dissimilarity. Our approach comprehensively captures kernel relationships, facilitating more efficient classification information extraction and improving clustering performance. By emphasizing the coherence between kernel correlation and dissimilarity, our method offers a more objective and transparent strategy for extracting non-linear information and significantly improving clustering precision, supported by theoretical rationale. We assess the performance of our algorithm on 13 challenging benchmark datasets, demonstrating its superiority over contemporary state-of-the-art MKKM techniques.

Edge-guided Low-light Image Enhancement with Inertial Bregman Alternating Linearized Minimization

Prior-based methods for low-light image enhancement often face challenges in extracting available prior information from dim images. To overcome this limitation, we introduce a simple yet effective Retinex model with the proposed edge extraction prior. More specifically, we design an edge extraction network to capture the fine edge features from the low-light image directly. Building upon the Retinex theory, we decompose the low-light image into its illumination and reflectance components and introduce an edge-guided Retinex model for enhancing low-light images. To solve the proposed model, we propose a novel inertial Bregman alternating linearized minimization algorithm. This algorithm addresses the optimization problem associated with the edge-guided Retinex model, enabling effective enhancement of low-light images. Through rigorous theoretical analysis, we establish the convergence properties of the algorithm. Besides, we prove that the proposed algorithm converges to a stationary point of the problem through nonconvex optimization theory. Furthermore, extensive experiments are conducted on multiple real-world low-light image datasets to demonstrate the efficiency and superiority of the proposed scheme.

Navigating Beyond Dropout: An Intriguing Solution Towards Generalizable Image Super Resolution

Deep learning has led to a dramatic leap on Single Image Super-Resolution (SISR) performances in recent years. %Despite the substantial advancement% While most existing work assumes a simple and fixed degradation model (e.g., bicubic downsampling), the research of Blind SR seeks to improve model generalization ability with unknown degradation. Recently, Kong et al pioneer the investigation of a more suitable training strategy for Blind SR using Dropout. Although such method indeed brings substantial generalization improvements via mitigating overfitting, we argue that Dropout simultaneously introduces undesirable side-effect that compromises model's capacity to faithfully reconstruct fine details. We show both the theoretical and experimental analyses in our paper, and furthermore, we present another easy yet effective training strategy that enhances the generalization ability of the model by simply modulating its first and second-order features statistics. Experimental results have shown that our method could serve as a model-agnostic regularization and outperforms Dropout on seven benchmark datasets including both synthetic and real-world scenarios.