arXiv subjects

Haibo Li

Publications and source records attributed to Haibo Li.

At least 37 records · Page 2Linked to original sources

arXiv2024

Scalable iterative data-adaptive RKHS regularization

We present iDARR, a scalable iterative Data-Adaptive RKHS Regularization method, for solving ill-posed linear inverse problems. The method searches for solutions in subspaces where the true solution can be identified, with the data-adaptive RKHS penalizing the spaces of small singular values. At the core of the method is a new generalized Golub-Kahan bidiagonalization procedure that recursively constructs orthonormal bases for a sequence of RKHS-restricted Krylov subspaces. The method is scalable with a complexity of $O(kmn)$ for $m$-by-$n$ matrices with $k$ denoting the iteration numbers. Numerical tests on the Fredholm integral equation and 2D image deblurring show that it outperforms the widely used $L^2$ and $l^2$ norms, producing stable accurate solutions consistently converging when the noise level decays.

math.NA↗

arXiv2023

Generalizing the SVD of a matrix under non-standard inner product and its applications to linear ill-posed problems

The singular value decomposition (SVD) of a matrix is a powerful tool for many matrix computation problems. In this paper, we consider generalizing the standard SVD to analyze and compute the regularized solution of linear ill-posed problems that arise from discretizing the first kind Fredholm integral equations. For the commonly used quadrature method for discretization, a regularizer of the form $\|x\|_{M}^2:=x^TMx$ should be exploited, where $M$ is symmetric positive definite. To handle this regularizer, we give the weighted SVD (WSVD) of a matrix under the $M$-inner product. Several important applications of WSVD, such as low-rank approximation and solving the least squares problems with minimum $\|\cdot\|_M$-norm, are studied. We propose the weighted Golub-Kahan bidiagonalization (WGKB) to compute several dominant WSVD components and a corresponding weighted LSQR algorithm to iteratively solve the least squares problem. All the above tools and methods are used to analyze and solve linear ill-posed problems with the regularizer $\|x\|_{M}^2$. A WGKB-based subspace projection regularization method is proposed to efficiently compute a good regularized solution, which can incorporate the prior information about $x$ encoded by the regularizer $\|x\|_{M}^2$. Several numerical experiments are performed to illustrate the fruitfulness of our methods.

math.NA↗

arXiv2023

A preconditioned Krylov subspace method for linear inverse problems with general-form Tikhonov regularization

Tikhonov regularization is a widely used technique in solving inverse problems that can enforce prior properties on the desired solution. In this paper, we propose a Krylov subspace based iterative method for solving linear inverse problems with general-form Tikhonov regularization term $x^TMx$, where $M$ is a positive semi-definite matrix. An iterative process called the preconditioned Golub-Kahan bidiagonalization (pGKB) is designed, which implicitly utilizes a proper preconditioner to generate a series of solution subspaces with desirable properties encoded by the regularizer $x^TMx$. Based on the pGKB process, we propose an iterative regularization algorithm via projecting the original problem onto small dimensional solution subspaces. We analyze regularization effect of this algorithm, including the incorporation of prior properties of the desired solution into the solution subspace and the semi-convergence behavior of regularized solution. To overcome instabilities caused by semi-convergence, we further propose two pGKB based hybrid regularization algorithms. All the proposed algorithms are tested on both small-scale and large-scale linear inverse problems. Numerical results demonstrate that these iterative algorithms exhibit excellent performance, outperforming other state-of-the-art algorithms in some cases.

math.NA↗

arXiv2022

Backward error analysis of the Lanczos bidiagonalization with reorthogonalization

The $k$-step Lanczos bidiagonalization reduces a matrix $A\in\mathbb{R}^{m\times n}$ into a bidiagonal form $B_k\in\mathbb{R}^{(k+1)\times k}$ while generates two orthonormal matrices $U_{k+1}\in\mathbb{R}^{m\times (k+1)}$ and $V_{k+1}\in\mathbb{R}^{n\times {(k+1)}}$. However, any practical implementation of the algorithm suffers from loss of orthogonality of $U_{k+1}$ and $V_{k+1}$ due to the presence of rounding errors, and several reorthogonalization strategies are proposed to maintain some level of orthogonality. In this paper, by writing various reorthogonalization strategies in a general form we make a backward error analysis of the Lanczos bidiagonalization with reorthogonalization (LBRO). Our results show that the computed $B_k$ by the $k$-step LBRO of $A$ with starting vector $b$ is the exact one generated by the $k$-step Lanczos bidiagonalization of $A+E$ with starting vector $b+δ_{b}$ (denoted by LB($A+E,b+δ_{b}$)), where the 2-norm of perturbation vector/matrix $δ_{b}$ and $E$ depend on the roundoff unit and orthogonality levels of $U_{k+1}$ and $V_{k+1}$. The results also show that the 2-norm of $U_{k+1}-\bar{U}_{k+1}$ and $V_{k+1}-\bar{V}_{k+1}$ are controlled by the orthogonality levels of $U_{k+1}$ and $V_{k+1}$, respectively, where $\bar{U}_{k+1}$ and $\bar{V}_{k+1}$ are the two orthonormal matrices generated by the $k$-step LB($A+E,b+δ_{b}$) in exact arithmetic. Thus the $k$-step LBRO is mixed forward-backward stable as long as the orthogonality of $U_{k+1}$ and $V_{k+1}$ are good enough. We use this result to investigate the backward stability of LBRO based SVD computation algorithm and LSQR algorithm. Numerical experiments are made to confirm our results.

math.NA↗

arXiv2022

Substrate-mediated Borophane Polymorphs through Hydrogenation of Two-dimensional Boron Sheets

Two-dimensional boron monolayer (borophene) stands out from the two-dimensional atomic layered materials due to its structural flexibility, tunable electronic and mechanical properties from a large number of allotropic materials. The stability of pristine borophene polymorphs could possibly be improved via hydrogenation with atomic hydrogen (referred to as borophane). However, the precise adsorption structures and the underlying mechanism are still elusive. Employing first-principles calculations, we demonstrate the optimal configurations of freestanding borophanes and the ones grown on metallic substrates. For freestanding β12 and χ3 borophenes, the energetically favored hydrogen adsorption sites are on the top of the boron atoms with CN=4 (CN: coordination number), while the best absorption sites for α' borophene are on the top of the boron atoms with CN=6. With various metal substrates, the hydrogenation configurations of borophene are modulated significantly, attributed to the chemical hybridization strength between B pz and H s orbitals. These findings provide a deep insight into the hydrogenating borophenes and facilitate the stabilization of two-dimensional boron polymorphs by engineering hydrogen adsorption sites and concentrations.

cond-mat.mtrl-sci↗

arXiv2022

The joint bidiagonalization method for large GSVD computations in finite precision

The joint bidiagonalization (JBD) method has been used to compute some extreme generalized singular values and vectors of a large regular matrix pair $\{A,L\}$, where we propose three approaches to compute approximate generalized singular values and vectors. We make a numerical analysis of the underlying JBD process and establish relationships between it and two mathematically equivalent Lanczos bidiagonalizations in finite precision. Based on the results of numerical analysis, we investigate the convergence of the approximate generalized singular values and vectors of $\{A,L\}$. The results show that, under some mild conditions, the semiorthogonality of Lanczos type vectors suffices to deliver approximate generalized singular values with the same accuracy as the full orthogonality does, meaning that it is only necessary to seek for efficient semiorthogonalization strategies for the JBD process. We also establish a sharp bound for the residual norm of an approximate generalized singular value and corresponding approximate right generalized singular vectors, which can reliably estimate the residual norm without explicitly computing the approximate right generalized singular vectors before the convergence occurs.

math.NA↗

arXiv2021

The joint bidiagonalization process with partial reorthogonalization

The joint bidiagonalization(JBD) process is a useful algorithm for the computation of the generalized singular value decomposition(GSVD) of a matrix pair. However, it always suffers from rounding errors, which causes the Lanczos vectors to loss their mutual orthogonality. In order to maintain some level of orthongonality, we present a semiorthogonalization strategy. Our rounding error analysis shows that the JBD process with the semiorthogonalization strategy can ensure that the convergence of the computed quantities is not affected by rounding errors and the final accuracy is high enough. Based on the semiorthogonalization strategy, we develop the joint bidiagonalization process with partial reorthogonalization(JBDPRO). In the JBDPRO algorithm, reorthogonalizations occur only when necessary, which saves a big amount of reorthogonalization work compared with the full reorthogonalization strategy. Numerical experiments illustrate our theory and algorithm.

math.NA↗

arXiv2020

On inner iterations of the joint bidiagonalization based algorithms for solving large scale ill-posed problems

The joint bidiagonalization process of a matrix pair $\{A,L\}$ can be used to develop iterative regularization algorithms for large scale ill-posed problems in general-form Tikhonov regularization $\min_x\left\{\|Ax-b\|_{2}^2+λ^2\|Lx\|_{2}^2\right\}$ or the essentially equivalent one $\min\|Lx\|_{2} \ \mbox{\rm s.t.} \ x\in\mathcal{S} = \{x|\ \|Ax-b\|_{2}\leq η\|e\|_{2}\}$, where $e$ is a Gaussian white noise, $L$ is a regularization matrix and $η>1$ slightly. A bottleneck of the algorithms is that a large scale inner least squares problem with $(A^{T}, L^{T})^{T}$ as the coefficient matrix must be solved at each outer iteration, which may be costly, especially when the solution accuracy of these problems is high. In this paper, we give a detailed investigation on the solution accuracy requirement on the inner least squares problems and propose a practical stopping criterion for inner iterations. The results show that for ill-posed problems with not too small noise levels, the solution accuracy of the inner least squares problems can be relaxed considerably while it will not reduce the accuracy of regularized solutions, thus the overall efficiency of the algorithms can be improved substantially. Numerical experiments are made to illustrate our results and show some numerical performance of the algorithms.

math.NA↗

arXiv2018

Macro pose based non-invasive thermal comfort perception for energy efficiency

Individual thermal comfort perception gives important feedback signals for energy efficient control of smart buildings. However, there is no effective method to measure real-time thermal comfort status of individual occupant until now. For overcoming this challenge, a novel macro posed based non-invasive perception method for thermal comfort (NIMAP) was presented. The occupant pose images were captured by normal phone camera (computer or cell phone) and the corresponding 2D coordinates can be obtained. Based on this, a novel pose recognition algorithm for thermal comfort, including 12 sub-algorithms, was presented. The 12 thermal comfort related macro poses can be recognized. Further, based on Fanger theory, 369 subjects were invited for subjective questionnaire survey. 3 human occupants participated in the validation of the proposed method and massive data were collected. All the 12 thermal comfort related poses can be recognized effectively.

cs.HC↗

arXiv2018

Non-invasive measuring method of skin temperature based on skin sensitivity index and deep learning

In human-centered intelligent building, real-time measurements of human thermal comfort play critical roles and supply feedback control signals for building heating, ventilation, and air conditioning (HVAC) systems. Due to the challenges of intra- and inter-individual differences and skin subtleness variations, there is no satisfactory solution for thermal comfort measurements until now. In this paper, a non-invasive measuring method based on skin sensitivity index and deep learning (NISDL) was proposed to measure real-time skin temperature. A new evaluating index, named skin sensitivity index (SSI), was defined to overcome individual differences and skin subtleness variations. To illustrate the effectiveness of SSI proposed, two multi-layers deep learning framework (NISDL method I and II) was designed and the DenseNet201 was used for extracting features from skin images. The partly personal saturation temperature (NIPST) algorithm was use for algorithm comparisons. Another deep learning algorithm without SSI (DL) was also generated for algorithm comparisons. Finally, a total of 1.44 million image data was used for algorithm validation. The results show that 55.6180% and 52.2472% error values (NISDL method I, II) are scattered at [0, 0.25), and the same error intervals distribution of NIPST is 35.3933%.

cs.CV↗

arXiv2018

Non-invasive thermal comfort perception based on subtleness magnification and deep learning for energy efficiency

Human thermal comfort measurement plays a critical role in giving feedback signals for building energy efficiency. A non-invasive measuring method based on subtleness magnification and deep learning (NIDL) was designed to achieve a comfortable, energy efficient built environment. The method relies on skin feature data, e.g., subtle motion and texture variation, and a 315-layer deep neural network for constructing the relationship between skin features and skin temperature. A physiological experiment was conducted for collecting feature data (1.44 million) and algorithm validation. The non-invasive measurement algorithm based on a partly-personalized saturation temperature model (NIPST) was used for algorithm performance comparisons. The results show that the mean error and median error of the NIDL are 0.4834 Celsius and 0.3464 Celsius which is equivalent to accuracy improvements of 16.28% and 4.28%, respectively.

cs.HC↗

arXiv2018

Expressway visibility estimation based on image entropy and piecewise stationary time series analysis

Vision-based methods for visibility estimation can play a critical role in reducing traffic accidents caused by fog and haze. To overcome the disadvantages of current visibility estimation methods, we present a novel data-driven approach based on Gaussian image entropy and piecewise stationary time series analysis (SPEV). This is the first time that Gaussian image entropy is used for estimating atmospheric visibility. To lessen the impact of landscape and sunshine illuminance on visibility estimation, we used region of interest (ROI) analysis and took into account relative ratios of image entropy, to improve estimation accuracy. We assume fog and haze cause blurred images and that fog and haze can be considered as a piecewise stationary signal. We used piecewise stationary time series analysis to construct the piecewise causal relationship between image entropy and visibility. To obtain a real-world visibility measure during fog and haze, a subjective assessment was established through a study with 36 subjects who performed visibility observations. Finally, a total of two million videos were used for training the SPEV model and validate its effectiveness. The videos were collected from the constantly foggy and hazy Tongqi expressway in Jiangsu, China. The contrast model of visibility estimation was used for algorithm performance comparison, and the validation results of the SPEV model were encouraging as 99.14% of the relative errors were less than 10%.

cs.CV↗

arXiv2016

Leveraging Mid-Level Deep Representations For Predicting Face Attributes in the Wild

Predicting facial attributes from faces in the wild is very challenging due to pose and lighting variations in the real world. The key to this problem is to build proper feature representations to cope with these unfavourable conditions. Given the success of Convolutional Neural Network (CNN) in image classification, the high-level CNN feature, as an intuitive and reasonable choice, has been widely utilized for this problem. In this paper, however, we consider the mid-level CNN features as an alternative to the high-level ones for attribute prediction. This is based on the observation that face attributes are different: some of them are locally oriented while others are globally defined. Our investigations reveal that the mid-level deep representations outperform the prediction accuracy achieved by the (fine-tuned) high-level abstractions. We empirically demonstrate that the midlevel representations achieve state-of-the-art prediction performance on CelebA and LFWA datasets. Our investigations also show that by utilizing the mid-level representations one can employ a single deep network to achieve both face recognition and attribute prediction.

cs.CV↗

arXiv2016

Face Attribute Prediction Using Off-the-Shelf CNN Features

Predicting attributes from face images in the wild is a challenging computer vision problem. To automatically describe face attributes from face containing images, traditionally one needs to cascade three technical blocks --- face localization, facial descriptor construction, and attribute classification --- in a pipeline. As a typical classification problem, face attribute prediction has been addressed using deep learning. Current state-of-the-art performance was achieved by using two cascaded Convolutional Neural Networks (CNNs), which were specifically trained to learn face localization and attribute description. In this paper, we experiment with an alternative way of employing the power of deep representations from CNNs. Combining with conventional face localization techniques, we use off-the-shelf architectures trained for face recognition to build facial descriptors. Recognizing that the describable face attributes are diverse, our face descriptors are constructed from different levels of the CNNs for different attributes to best facilitate face attribute prediction. Experiments on two large datasets, LFWA and CelebA, show that our approach is entirely comparable to the state-of-the-art. Our findings not only demonstrate an efficient face attribute prediction approach, but also raise an important question: how to leverage the power of off-the-shelf CNN representations for novel tasks.

cs.CV↗

arXiv2015

Preprint Touch-less Interactive Augmented Reality Game on Vision Based Wearable Device

This is the preprint version of our paper on Personal and Ubiquitous Computing. There is an increasing interest in creating pervasive games based on emerging interaction technologies. In order to develop touch-less, interactive and augmented reality games on vision-based wearable device, a touch-less motion interaction technology is designed and evaluated in this work. Users interact with the augmented reality games with dynamic hands/feet gestures in front of the camera, which triggers the interaction event to interact with the virtual object in the scene. Three primitive augmented reality games with eleven dynamic gestures are developed based on the proposed touch-less interaction technology as proof. At last, a comparing evaluation is proposed to demonstrate the social acceptability and usability of the touch-less approach, running on a hybrid wearable framework or with Google Glass, as well as workload assessment, user's emotions and satisfaction.

cs.HC↗

arXiv2015

Search for low-mass Higgs and dark photons at BESIII

Many extensions of the Standard Model introduce a new type of weak-interacting degrees of freedom. These models are motivated by the results of recent experimental anomalies. Typical models, such as Next-to-Minimal Supersymmetric Standard Model and Light Hidden Dark-sector Model, introduce the possibilities of low-mass Higgs and dark bosons. The masses of such particles are expected to be few GeV and thus making them accessible at BESIII experiment, an $e^+e^-$ collider experiment running at tau-charm region. This report summarizes the recent results of low-mass Higgs and dark bosons searches at BESIII.

hep-ex↗

arXiv2015

Preprint Extending Touch-less Interaction on Vision Based Wearable Device

This is the preprint version of our paper on IEEE Virtual Reality Conference 2015. A touch-less interaction technology on vision based wearable device is designed and evaluated. Users interact with the application with dynamic hands/feet gestures in front of the camera. Several proof-of-concept prototypes with eleven dynamic gestures are developed based on the touch-less interaction. At last, a comparing user study evaluation is proposed to demonstrate the usability of the touch-less approach, as well as the impact on user's emotion, running on a wearable framework or Google Glass.

cs.HC↗

arXiv2015

Preprint Imagining In-Air Interaction for Hemiplegia Sufferer

This is the preprint version of our paper on 2015 International Conference on Virtual Rehabilitation (ICVR2015). In this paper, we described the imagination scenarios of a touch-less interaction technology for hemiplegia, which can support either hand or foot interaction with the smartphone or head mounted device (HMD). The computer vision interaction technology is implemented in our previous work, which provides a core support for gesture interaction by accurately detecting and tracking the hand or foot gesture. The patients interact with the application using hand/foot gesture motion in the camera view.

cs.HC↗