arXiv subjects

Jiaxin Xie

Publications and source records attributed to Jiaxin Xie.

At least 37 records · Page 2Linked to original sources

arXiv2024

Large Motion Video Autoencoding with Cross-modal Video VAE

Learning a robust video Variational Autoencoder (VAE) is essential for reducing video redundancy and facilitating efficient video generation. Directly applying image VAEs to individual frames in isolation can result in temporal inconsistencies and suboptimal compression rates due to a lack of temporal compression. Existing Video VAEs have begun to address temporal compression; however, they often suffer from inadequate reconstruction performance. In this paper, we present a novel and powerful video autoencoder capable of high-fidelity video encoding. First, we observe that entangling spatial and temporal compression by merely extending the image VAE to a 3D VAE can introduce motion blur and detail distortion artifacts. Thus, we propose temporal-aware spatial compression to better encode and decode the spatial information. Additionally, we integrate a lightweight motion compression model for further temporal compression. Second, we propose to leverage the textual information inherent in text-to-video datasets and incorporate text guidance into our model. This significantly enhances reconstruction quality, particularly in terms of detail preservation and temporal stability. Third, we further improve the versatility of our model through joint training on both images and videos, which not only enhances reconstruction quality but also enables the model to perform both image and video autoencoding. Extensive evaluations against strong recent baselines demonstrate the superior performance of our method. The project website can be found at~\href{https://yzxing87.github.io/vae/}{https://yzxing87.github.io/vae/}.

cs.CV↗

arXiv2024

A distributed Douglas-Rachford splitting method for solving linear constrained multi-block weakly convex problems

In recent years, a distributed Douglas-Rachford splitting method (DDRSM) has been proposed to tackle multi-block separable convex optimization problems. This algorithm offers relatively easier subproblems and greater efficiency for large-scale problems compared to various augmented-Lagrangian-based parallel algorithms. Building upon this, we explore the extension of DDRSM to weakly convex cases. By assuming weak convexity of the objective function and introducing an error bound assumption, we demonstrate the linear convergence rate of DDRSM. Some promising numerical experiments involving compressed sensing and robust alignment of structures across images (RASL) show that DDRSM has advantages over augmented-Lagrangian-based algorithms, even in weakly convex scenarios.

math.OC↗

arXiv2024

On greedy multi-step inertial randomized Kaczmarz method for solving linear systems

The multi-step inertial randomized Kaczmarz (MIRK) method is an iterative method for solving large-scale linear systems. In this paper, we enhance the MIRK method by incorporating the greedy probability criterion, coupled with the introduction of a tighter threshold parameter for this criterion. We prove that the proposed greedy MIRK (GMIRK) method enjoys an improved deterministic linear convergence compared to both the MIRK method and the greedy randomized Kaczmarz method. Furthermore, we exhibit that the multi-step inertial extrapolation approach can be geometrically interpreted as an orthogonal projection method, and establish its relationship with the sketch-and-project method in (SIAM J. Matrix Anal. Appl. 36(4):1660-1690, 2015) and the oblique projection technique in (Results Appl. Math. 16:100342, 2022). Numerical experiments are provided to confirm our results.

math.NA↗

arXiv2024

On adaptive stochastic heavy ball momentum for solving linear systems

The stochastic heavy ball momentum (SHBM) method has gained considerable popularity as a scalable approach for solving large-scale optimization problems. However, one limitation of this method is its reliance on prior knowledge of certain problem parameters, such as singular values of a matrix. In this paper, we propose an adaptive variant of the SHBM method for solving stochastic problems that are reformulated from linear systems using user-defined distributions. Our adaptive SHBM (ASHBM) method utilizes iterative information to update the parameters, addressing an open problem in the literature regarding the adaptive learning of momentum parameters. We prove that our method converges linearly in expectation, with a better convergence bound compared to the basic method. Notably, we demonstrate that the deterministic version of our ASHBM algorithm can be reformulated as a variant of the conjugate gradient (CG) method, inheriting many of its appealing properties, such as finite-time convergence. Consequently, the ASHBM method can be further generalized to develop a brand-new framework of the stochastic CG (SCG) method for solving linear systems. Our theoretical results are supported by numerical experiments.

math.OC↗

arXiv2024

Randomized Douglas-Rachford methods for linear systems: Improved accuracy and efficiency

The Douglas-Rachford (DR) method is a widely used method for finding a point in the intersection of two closed convex sets (feasibility problem). However, the method converges weakly and the associated rate of convergence is hard to analyze in general. In addition, the direct extension of the DR method for solving more-than-two-sets feasibility problems, called the $r$-sets-DR method, is not necessarily convergent. To improve the efficiency of the optimization algorithms, the introduction of randomization and the momentum technique has attracted increasing attention. In this paper, we propose the randomized $r$-sets-DR (RrDR) method for solving the feasibility problem derived from linear systems, showing the benefit of the randomization as it brings linear convergence in expectation to the otherwise divergent $r$-sets-DR method. Furthermore, the convergence rate does not depend on the dimension of the coefficient matrix. We also study RrDR with heavy ball momentum and establish its accelerated rate. Numerical experiments are provided to confirm our results and demonstrate the notable improvements in accuracy and efficiency of the DR method, brought by the randomization and the momentum technique.

math.OC↗

arXiv2023

On the convergence analysis of the greedy randomized Kaczmarz method

In this paper, we analyze the greedy randomized Kaczmarz (GRK) method proposed in Bai and Wu (SIAM J. Sci. Comput., 40(1):A592--A606, 2018) for solving linear systems. We develop more precise greedy probability criteria to effectively select the working row from the coefficient matrix. Notably, we prove that the linear convergence of the GRK method is deterministic and demonstrate that using a tighter threshold parameter can lead to a faster convergence rate. Our result revises existing convergence analyses, which are solely based on the expected error by realizing that the iterates of the GRK method are random variables. Consequently, we obtain an improved iteration complexity for the GRK method. Moreover, the Polyak's heavy ball momentum technique is incorporated to improve the performance of the GRK method. We propose a refined convergence analysis, compared with the technique used in Loizou and Richtárik (Comput. Optim. Appl., 77(3):653--710, 2020), of momentum variants of randomized iterative methods, which shows that the proposed GRK method with momentum (mGRK) also enjoys a deterministic linear convergence. Numerical experiments show that the mGRK method is more efficient than the GRK method.

math.NA↗

arXiv2023

Randomized Kaczmarz method with adaptive stepsizes for inconsistent linear systems

We investigate the randomized Kaczmarz method that adaptively updates the stepsize using readily available information for solving inconsistent linear systems. A novel geometric interpretation is provided which shows that the proposed method can be viewed as an orthogonal projection method in some sense. We prove that this method converges linearly in expectation to the unique minimum Euclidean norm least-squares solution of the linear system, and provide a tight upper bound for the convergence of the proposed method. Numerical experiments are also given to illustrate the theoretical results.

math.NA↗

arXiv2022

High-fidelity 3D GAN Inversion by Pseudo-multi-view Optimization

We present a high-fidelity 3D generative adversarial network (GAN) inversion framework that can synthesize photo-realistic novel views while preserving specific details of the input image. High-fidelity 3D GAN inversion is inherently challenging due to the geometry-texture trade-off in 3D inversion, where overfitting to a single view input image often damages the estimated geometry during the latent optimization. To solve this challenge, we propose a novel pipeline that builds on the pseudo-multi-view estimation with visibility analysis. We keep the original textures for the visible parts and utilize generative priors for the occluded parts. Extensive experiments show that our approach achieves advantageous reconstruction and novel view synthesis quality over state-of-the-art methods, even for images with out-of-distribution textures. The proposed pipeline also enables image attribute editing with the inverted latent code and 3D-aware texture modification. Our approach enables high-fidelity 3D rendering from a single image, which is promising for various applications of AI-generated 3D content.

cs.CV↗

arXiv2022

A greedy randomized average block projection method for linear feasibility problems

The randomized projection (RP) method is a simple iterative scheme for solving linear feasibility problems and has recently gained popularity due to its speed and low memory requirement. This paper develops an accelerated variant of the standard RP method by using two ingredients: the greedy probability criterion and the average block approach, and obtains a greedy randomized average block projection (GRABP) method for solving large-scale systems of linear inequalities. We prove that this method converges linearly in expectation under different choices of extrapolated stepsizes. Numerical experiments on both randomly generated and real-world data show the advantage of GRABP over several state-of-the-art solvers, such as the randomized projection (RP) method, the sampling Kaczmarz Motzkin (SKM) method, the generalized SKM (GSKM) method, and the Nesterov acceleration of SKM method.

math.OC↗

arXiv2022

On pseudoinverse-free randomized methods for linear systems: Unified framework and acceleration

We present a new framework for the analysis and design of randomized algorithms for solving various types of linear systems, including consistent or inconsistent, full rank or rank-deficient. Our method is formulated with four randomized sampling parameters, which allows the method to cover many existing randomization algorithms within a unified framework, including the doubly stochastic Gauss-Seidel, randomized Kaczmarz method, randomized coordinate descent method, and Gaussian Kaczmarz method. Compared with the projection-based block algorithms where a pseudoinverse for solving a least-squares problem is utilized at each iteration, our design is pseudoinverse-free. Furthermore, the flexibility of the new approach also enables the design of a number of new methods as special cases. Polyak's heavy ball momentum technique is also introduced in our framework for improving the convergence behavior of the method. We prove the global linear convergence rates of our method as well as an accelerated linear rate for the case of the norm of expected iterates. Finally, numerical experiments are provided to confirm our results.

math.OC↗

arXiv2022

Shape from Polarization for Complex Scenes in the Wild

We present a new data-driven approach with physics-based priors to scene-level normal estimation from a single polarization image. Existing shape from polarization (SfP) works mainly focus on estimating the normal of a single object rather than complex scenes in the wild. A key barrier to high-quality scene-level SfP is the lack of real-world SfP data in complex scenes. Hence, we contribute the first real-world scene-level SfP dataset with paired input polarization images and ground-truth normal maps. Then we propose a learning-based framework with a multi-head self-attention module and viewing encoding, which is designed to handle increasing polarization ambiguities caused by complex materials and non-orthographic projection in scene-level SfP. Our trained model can be generalized to far-field outdoor scenes as the relationship between polarized light and surface normals is not affected by distance. Experimental results demonstrate that our approach significantly outperforms existing SfP models on two datasets. Our dataset and source code will be publicly available at https://github.com/ChenyangLEI/sfp-wild

cs.CV↗

arXiv2021

Dual-Camera Super-Resolution with Aligned Attention Modules

We present a novel approach to reference-based super-resolution (RefSR) with the focus on dual-camera super-resolution (DCSR), which utilizes reference images for high-quality and high-fidelity results. Our proposed method generalizes the standard patch-based feature matching with spatial alignment operations. We further explore the dual-camera super-resolution that is one promising application of RefSR, and build a dataset that consists of 146 image pairs from the main and telephoto cameras in a smartphone. To bridge the domain gaps between real-world images and the training images, we propose a self-supervised domain adaptation strategy for real-world images. Extensive experiments on our dataset and a public benchmark demonstrate clear improvement achieved by our method over state of the art in both quantitative evaluation and visual comparisons.

cs.CV↗

arXiv2021

Upper and Lower bounds for matrix discrepancy

The aim of this paper is to study the matrix discrepancy problem. Assume that $ξ_1,\ldots,ξ_n$ are independent scalar random variables with finite support and $\mathbf{u}_1,\ldots,\mathbf{u}_n\in \mathbb{C}^d$. Let $\mathcal{C}_0$ be the minimal constant for which the following holds: \[ {\rm Disc}(\mathbf{u}_1\mathbf{u}_1^*,\ldots,\mathbf{u}_n\mathbf{u}_n^*; ξ_1,\ldots,ξ_n)\,\,:=\,\,\min_{\varepsilon_1\in \mathcal{S}_1,\ldots,\varepsilon_n\in \mathcal{S}_n}\bigg\|\sum_{i=1}^n\mathbb{E}[ξ_i]\mathbf{u}_i\mathbf{u}_i^*-\sum_{i=1}^n\varepsilon_i\mathbf{u}_i\mathbf{u}_i^*\bigg\|\leq \mathcal{C}_0\cdotσ, \] where $σ^2 = \big\|\sum_{i=1}^n \mathbf{Var}[ξ_i](\mathbf{u}_i\mathbf{u}_i^*)^2\big\|$ and $\mathcal{S}_j$ denotes the support of $ξ_j, j=1,\ldots,n$. Motivated by the technology developed by Bownik, Casazza, Marcus, and Speegle, we prove $\mathcal{C}_0\leq 3$. This improves Kyng, Luh and Song's method with which $\mathcal{C}_0\leq 4$. For the case where $\{\mathbf{u}_i\}_{i=1}^n\subset \mathbb{C}^d$ is a unit-norm tight frame with $ n\leq 2d-1$ and $ξ_1,\ldots,ξ_n$ are independent Rademacher random variables, we present the exact value of ${\rm Disc}(\mathbf{u}_1\mathbf{u}_1^*,\ldots,\mathbf{u}_n\mathbf{u}_n^*; ξ_1,\ldots,ξ_n)=\sqrt{\frac{n}{d}}\cdotσ$, which implies $\mathcal{C}_0\geq \sqrt{2}$.

math.CO↗

arXiv2021

Graph Sparsification by Universal Greedy Algorithms

Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications, such as simplification of social networks, least squares problems, numerical solution of symmetric positive definite linear systems and etc. In this paper, inspired by the well-known sparse signal recovery algorithm called orthogonal matching pursuit (OMP), we introduce a deterministic, greedy edge selection algorithm called universal greedy approach (UGA) for graph sparsification. For a general spectral sparsification problem, e.g., positive subset selection problem from a set of $m$ vectors from $\mathbb{R}^n$, we propose a nonnegative UGA algorithm which needs $O(mn^2+ n^3/ε^2)$ time to find a $\frac{1+ε/β}{1-ε/β}$-spectral sparsifier with positive coefficients with sparsity $\le\lceil\frac{n}{ε^2}\rceil$, where $β$ is the ratio between the smallest length and largest length of the vectors. The convergence of the nonnegative UGA algorithm will be established. For the graph sparsification problem, another UGA algorithm will be proposed which can output a $\frac{1+O(ε)}{1-O(ε)}$-spectral sparsifier with $\lceil\frac{n}{ε^2}\rceil$ edges in $O(m+n^2/ε^2)$ time from a graph with $m$ edges and $n$ vertices under some mild assumptions. This is a linear time algorithm in terms of the number of edges that the community of graph sparsification is looking for. The best result in the literature to the knowledge of the authors is the existence of a deterministic algorithm which is almost linear, i.e. $O(m^{1+o(1)})$ for some $o(1)=O(\frac{(\log\log(m))^{2/3}}{\log^{1/3}(m)})$. Finally, extensive experimental results, including applications to graph clustering and least squares regression, show the effectiveness of proposed approaches.

cs.DS↗

arXiv2020

A symmetric alternating minimization algorithm for total variation minimization

In this paper, we propose a novel symmetric alternating minimization algorithm to solve a broad class of total variation (TV) regularization problems. Unlike the usual $z^k\to x^k$ Gauss-Seidel cycle, the proposed algorithm performs the special $\overline{x}^{k}\to z^k\to x^k$ cycle. The main idea for our setting is the recent symmetric Gauss-Seidel (sGS) technique which is developed for solving the multi-block convex composite problem. This idea also enables us to build the equivalence between the proposed method and the well-known accelerated proximal gradient (APG) method. The faster convergence rate of the proposed algorithm can be directly obtained from the APG framework and numerical results including image denoising, image deblurring, and analysis sparse recovery problem demonstrate the effectiveness of the new algorithm.

cs.DS↗

arXiv2020

A note on restricted invertibility with weighted columns

The restricted invertibility theorem was originally introduced by Bourgain and Tzafriri in $1987$ and has been considered as one of the most celebrated theorems in geometry and analysis. In this note, we present weighted versions of this theorem with slightly better estimates. Particularly, we show that for any $A\in\mathbb{R}^{n\times m}$ and $k,r\in\mathbb{N}$ with $k\leq r\leq \mbox{rank}(A)$, there exists a subset $\mathcal{S}$ of size $k$ such that $σ_{\min}(A_{\mathcal{S}}W_{\mathcal{S}})^2\geq \frac{(\sqrt{r}-\sqrt{k-1})^2}{\|W^{-1}\|_F^{2}}\cdot\frac{r}{\sum_{i=1}^{r}σ_{i}(A)^{-2}}$, where $W=\mbox{diag}(w_1,\ldots,w_m)$ with $w_i$ being the weight of the $i$-th column of $A$. Our constructions are algorithmic and employ the interlacing families of polynomials developed by Marcus, Spielman, and Srivastava.

math.FA↗

arXiv2020

Depth Sensing Beyond LiDAR Range

Depth sensing is a critical component of autonomous driving technologies, but today's LiDAR- or stereo camera-based solutions have limited range. We seek to increase the maximum range of self-driving vehicles' depth perception modules for the sake of better safety. To that end, we propose a novel three-camera system that utilizes small field of view cameras. Our system, along with our novel algorithm for computing metric depth, does not require full pre-calibration and can output dense depth maps with practically acceptable accuracy for scenes and objects at long distances not well covered by most commercial LiDARs.

cs.CV↗

arXiv2020

Subset Selection for Matrices with Fixed Blocks

Subset selection for matrices is the task of extracting a column sub-matrix from a given matrix $B\in\mathbb{R}^{n\times m}$ with $m>n$ such that the pseudoinverse of the sampled matrix has as small Frobenius or spectral norm as possible. In this paper, we consider a more general problem of subset selection for matrices that allows a block to be fixed at the beginning. Under this setting, we provide a deterministic method for selecting a column sub-matrix from $B$. We also present a bound for both the Frobenius and spectral norms of the pseudoinverse of the sampled matrix, showing that the bound is asymptotically optimal. The main technology for proving this result is the interlacing families of polynomials developed by Marcus, Spielman, and Srivastava. This idea also results in a deterministic greedy selection algorithm that produces the sub-matrix promised by our result.

cs.DS↗