Yang Wang

Mark Iwen, Aditya Viswanathan, Yang Wang

We develop a fast phase retrieval method which can utilize a large class of local phaseless correlation-based measurements in order to recover a given signal ${\bf x} \in \mathbb{C}^d$ (up to an unknown global phase) in near-linear $\mathcal{O} \left( d \log^4 d \right)$-time. Accompanying theoretical analysis proves that the proposed algorithm is guaranteed to deterministically recover all signals ${\bf x}$ satisfying a natural flatness (i.e., non-sparsity) condition for a particular choice of deterministic correlation-based measurements. A randomized version of these same measurements is then shown to provide nonuniform probabilistic recovery guarantees for arbitrary signals ${\bf x} \in \mathbb{C}^d$. Numerical experiments demonstrate the method's speed, accuracy, and robustness in practice -- all code is made publicly available. Finally, we conclude by developing an extension of the proposed method to the sparse phase retrieval problem; specifically, we demonstrate a sublinear-time compressive phase retrieval algorithm which is guaranteed to recover a given $s$-sparse vector ${\bf x} \in \mathbb{C}^d$ with high probability in just $\mathcal{O}(s \log^5 s \cdot \log d)$-time using only $\mathcal{O}(s \log^4 s \cdot \log d)$ magnitude measurements. In doing so we demonstrate the existence of compressive phase retrieval algorithms with near-optimal linear-in-sparsity runtime complexities.

Xin Di, Long Peng, Peizhe Xia et al.

Burst super-resolution aims to reconstruct high-resolution images with higher quality and richer details by fusing the sub-pixel information from multiple burst low-resolution frames. In BusrtSR, the key challenge lies in extracting the base frame's content complementary sub-pixel details while simultaneously suppressing high-frequency noise disturbance. Existing methods attempt to extract sub-pixels by modeling inter-frame relationships frame by frame while overlooking the mutual correlations among multi-current frames and neglecting the intra-frame interactions, leading to inaccurate and noisy sub-pixels for base frame super-resolution. Further, existing methods mainly employ static upsampling with fixed parameters to improve spatial resolution for all scenes, failing to perceive the sub-pixel distribution difference across multiple frames and cannot balance the fusion weights of different frames, resulting in over-smoothed details and artifacts. To address these limitations, we introduce a novel Query Mamba Burst Super-Resolution (QMambaBSR) network, which incorporates a Query State Space Model (QSSM) and Adaptive Up-sampling module (AdaUp). Specifically, based on the observation that sub-pixels have consistent spatial distribution while random noise is inconsistently distributed, a novel QSSM is proposed to efficiently extract sub-pixels through inter-frame querying and intra-frame scanning while mitigating noise interference in a single step. Moreover, AdaUp is designed to dynamically adjust the upsampling kernel based on the spatial distribution of multi-frame sub-pixel information in the different burst scenes, thereby facilitating the reconstruction of the spatial arrangement of high-resolution details. Extensive experiments on four popular synthetic and real-world benchmarks demonstrate that our method achieves a new state-of-the-art performance.

Yang Wang, Zhiqiang Xu

In this paper, we study the performance of the PCM scheme with linear quantization rule for quantizing finite unit-norm tight frame expansions for $\R^d$ and derive the PCM quantization error without the White Noise Hypothesis. We prove that for the class of unit norm tight frames derived from uniform frame paths the quantization error has an upper bound of $O(δ^{3/2})$ regardless of the frame redundancy. This is achieved using some of the techniques developed by Güntürk in his study of Sigma-Delta quantization. Using tools of harmonic analysis we show that this upper bound is sharp for $d=2$. A consequence of this result is that, unlike with Sigma-Delta quantization, the error for PCM quantization in general does not diminish to zero as one increases the frame redundancy. We extend the result to high dimension and show that the PCM quantization error has an upper bound $O(δ^{(d+1)/2})$ for asymptopitcally equidistributed unit-norm tight frame of $\R^{d}$.

Yang Wang, Zhiqiang Xu

The regularity of refinable functions has been studied extensively in the past. A classical result by Daubechies and Lagarias states that a compactly supported refinable function in $\R$ of finite mask with integer dilation and translations cannot be in $C^\infty$. A bound on the regularity based on the eigenvalues of certain matrices associated with the refinement equation is also given. Surprisingly this fundamental classical result has not been proved in the more general settings, such as in higher dimensions or when the dilation is not an integer. In this paper we extend this classical result to the most general setting for arbitrary dimension, dilation and translations.

Yingda Yin, Yang Wang, He Wang et al.

Estimating the 3DoF rotation from a single RGB image is an important yet challenging problem. Probabilistic rotation regression has raised more and more attention with the benefit of expressing uncertainty information along with the prediction. Though modeling noise using Gaussian-resembling Bingham distribution and matrix Fisher distribution is natural, they are shown to be sensitive to outliers for the nature of quadratic punishment to deviations. In this paper, we draw inspiration from multivariate Laplace distribution and propose a novel Rotation Laplace distribution on SO(3). Rotation Laplace distribution is robust to the disturbance of outliers and enforces much gradient to the low-error region, resulting in a better convergence. Our extensive experiments show that our proposed distribution achieves state-of-the-art performance for rotation regression tasks over both probabilistic and non-probabilistic baselines. Our project page is at https://pku-epic.github.io/RotationLaplace.

Long Peng, Yang Cao, Yuejin Sun et al.

JPEG is a widely used compression scheme to efficiently reduce the volume of transmitted images. The artifacts appear among blocks due to the information loss, which not only affects the quality of images but also harms the subsequent high-level tasks in terms of feature drifting. High-level vision models trained on high-quality images will suffer performance degradation when dealing with compressed images, especially on mobile devices. Numerous learning-based JPEG artifact removal methods have been proposed to handle visual artifacts. However, it is not an ideal choice to use these JPEG artifact removal methods as a pre-processing for compressed image classification for the following reasons: 1. These methods are designed for human vision rather than high-level vision models; 2. These methods are not efficient enough to serve as pre-processing on resource-constrained devices. To address these issues, this paper proposes a novel lightweight AFD module to boost the performance of pre-trained image classification models when facing compressed images. First, a FDE-Net is devised to generate the spatial-wise FDM in the DCT domain. Next, the estimated FDM is transmitted to the FE-Net to generate the mapping relationship between degraded features and corresponding high-quality features. A simple but effective RepConv block equipped with structural re-parameterization is utilized in FE-Net, which enriches feature representation in the training phase while maintaining efficiency in the deployment phase. After training on limited compressed images, the AFD-Module can serve as a "plug-and-play" model for pre-trained classification models to improve their performance on compressed images. Experiments demonstrate that our proposed AFD module can comprehensively improve the accuracy of the pre-trained classification models and significantly outperform the existing methods.

Long Peng, Yang Cao, Renjing Pei et al.

Real-SR endeavors to produce high-resolution images with rich details while mitigating the impact of multiple degradation factors. Although existing methods have achieved impressive achievements in detail recovery, they still fall short when addressing regions with complex gradient arrangements due to the intensity-based linear weighting feature extraction manner. Moreover, the stochastic artifacts introduced by degradation cues during the imaging process in real LR increase the disorder of the overall image details, further complicating the perception of intrinsic gradient arrangement. To address these challenges, we innovatively introduce kernel-wise differential operations within the convolutional kernel and develop several learnable directional gradient convolutions. These convolutions are integrated in parallel with a novel linear weighting mechanism to form an Adaptive Directional Gradient Convolution (DGConv), which adaptively weights and fuses the basic directional gradients to improve the gradient arrangement perception capability for both regular and irregular textures. Coupled with DGConv, we further devise a novel equivalent parameter fusion method for DGConv that maintains its rich representational capabilities while keeping computational costs consistent with a single Vanilla Convolution (VConv), enabling DGConv to improve the performance of existing super-resolution networks without incurring additional computational expenses. To better leverage the superiority of DGConv, we further develop an Adaptive Information Interaction Block (AIIBlock) to adeptly balance the enhancement of texture and contrast while meticulously investigating the interdependencies, culminating in the creation of a DGPNet for Real-SR through simple stacking. Comparative results with 15 SOTA methods across three public datasets underscore the effectiveness and efficiency of our proposed approach.

Long Peng, Xin Di, Zhanfeng Feng et al.

Image restoration aims to recover details and enhance contrast in degraded images. With the growing demand for high-quality imaging (\textit{e.g.}, 4K and 8K), achieving a balance between restoration quality and computational efficiency has become increasingly critical. Existing methods, primarily based on CNNs, Transformers, or their hybrid approaches, apply uniform deep representation extraction across the image. However, these methods often struggle to effectively model long-range dependencies and largely overlook the spatial characteristics of image degradation (regions with richer textures tend to suffer more severe damage), making it hard to achieve the best trade-off between restoration quality and efficiency. To address these issues, we propose a novel texture-aware image restoration method, TAMambaIR, which simultaneously perceives image textures and achieves a trade-off between performance and efficiency. Specifically, we introduce a novel Texture-Aware State Space Model, which enhances texture awareness and improves efficiency by modulating the transition matrix of the state-space equation and focusing on regions with complex textures. Additionally, we design a {Multi-Directional Perception Block} to improve multi-directional receptive fields while maintaining low computational overhead. Extensive experiments on benchmarks for image super-resolution, deraining, and low-light image enhancement demonstrate that TAMambaIR achieves state-of-the-art performance with significantly improved efficiency, establishing it as a robust and efficient framework for image restoration.

Zhanwen Liu, Sai Zhou, Yuchao Dai et al.

All-in-One image restoration aims to address multiple image degradation problems using a single model, offering a more practical and versatile solution compared to designing dedicated models for each degradation type. Existing approaches typically rely on Degradation-specific models or coarse-grained degradation prompts to guide image restoration. However, they lack fine-grained modeling of degradation information and face limitations in balancing multi-task conflicts. To overcome these limitations, we propose DPMambaIR, a novel All-in-One image restoration framework that introduces a fine-grained degradation extractor and a Degradation-Aware Prompt State Space Model (DP-SSM). The DP-SSM leverages the fine-grained degradation features captured by the extractor as dynamic prompts, which are then incorporated into the state space modeling process. This enhances the model's adaptability to diverse degradation types, while a complementary High-Frequency Enhancement Block (HEB) recovers local high-frequency details. Extensive experiments on a mixed dataset containing seven degradation types show that DPMambaIR achieves the best performance, with 27.69dB and 0.893 in PSNR and SSIM, respectively. These results highlight the potential and superiority of DPMambaIR as a unified solution for All-in-One image restoration.

Gengyu Lin, Zhengyang Zhou, Qihe Huang et al.

Spatiotemporal learning plays a crucial role in mobile computing techniques to empower smart cites. While existing research has made great efforts to achieve accurate predictions on the overall dataset, they still neglect the significant performance heterogeneity across samples. In this work, we designate the performance heterogeneity as the reason for unfair spatiotemporal learning, which not only degrades the practical functions of models, but also brings serious potential risks to real-world urban applications. To fix this gap, we propose a model-independent Fairness-aware framework for SpatioTemporal Graph learning (FairSTG), which inherits the idea of exploiting advantages of well-learned samples to challenging ones with collaborative mix-up. Specifically, FairSTG consists of a spatiotemporal feature extractor for model initialization, a collaborative representation enhancement for knowledge transfer between well-learned samples and challenging ones, and fairness objectives for immediately suppressing sample-level performance heterogeneity. Experiments on four spatiotemporal datasets demonstrate that our FairSTG significantly improves the fairness quality while maintaining comparable forecasting accuracy. Case studies show FairSTG can counter both spatial and temporal performance heterogeneity by our sample-level retrieval and compensation, and our work can potentially alleviate the risks on spatiotemporal resource allocation for underrepresented urban regions.

Binglin Li, Mohammad Akbari, Jie Liang et al.

Recently many works attempt to develop image compression models based on deep learning architectures, where the uniform scalar quantizer (SQ) is commonly applied to the feature maps between the encoder and decoder. In this paper, we propose to incorporate trellis coded quantizer (TCQ) into a deep learning based image compression framework. A soft-to-hard strategy is applied to allow for back propagation during training. We develop a simple image compression model that consists of three subnetworks (encoder, decoder and entropy estimation), and optimize all of the components in an end-to-end manner. We experiment on two high resolution image datasets and both show that our model can achieve superior performance at low bit rates. We also show the comparisons between TCQ and SQ based on our proposed baseline model and demonstrate the advantage of TCQ.

Jian-Feng Cai, Lizhang Miao, Yang Wang et al.

We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value obtained from a spectral method can reconstruct a tensor of size $n\times n \times\cdots \times n$ tensor of ranks $(r,\cdots,r)$ with high probability from as few as $O((r^d+dnr)\log(d))$ entries. In the case of order 3 tensor, the entries can be asymptotically as few as $O(nr)$ for a low rank large tensor. We show the theoretical guarantee condition for the recovery. The analysis relies on the tensor restricted isometry property (tensor RIP) and the curvature of the low rank tensor manifold. Our algorithm is computationally efficient and easy to implement. Numerical results verify that the algorithms are able to recover a low rank tensor from minimum number of measurements. The experiments on hyperspectral images recovery also show that our algorithm is capable of real world signal processing problems.

Dong Mao, Yang Wang, Qiang Wu

We developed a new approach for the analysis of physiological time series. An iterative convolution filter is used to decompose the time series into various components. Statistics of these components are extracted as features to characterize the mechanisms underlying the time series. Motivated by the studies that show many normal physiological systems involve irregularity while the decrease of irregularity usually implies the abnormality, the statistics for "outliers" in the components are used as features measuring irregularity. Support vector machines are used to select the most relevant features that are able to differentiate the time series from normal and abnormal systems. This new approach is successfully used in the study of congestive heart failure by heart beat interval time series.

Bo Wahlberg, Stephen Boyd, Mariette Annergren et al.

We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between consecutive variable blocks. Examples of such problems include Fused Lasso estimation, total variation denoising, and multi-period portfolio optimization with transaction costs. In each iteration of our method, the first step involves separately optimizing over each variable block, which can be carried out in parallel. The second step is not separable in the variables, but can be carried out very efficiently. We apply the algorithm to segmentation of data based on changes inmean (l_1 mean filtering) or changes in variance (l_1 variance filtering). In a numerical example, we show that our implementation is around 10000 times faster compared with the generic optimization solver SDPT3.