arXiv subjects

Guoen Hu

Publications and source records attributed to Guoen Hu.

At least 19 recordsLinked to original sources

arXiv2024

An endpoint estimate for the maximal Calder\'on commutator with rough kernel

In this paper, the authors consider the endpoint estimates for the maximal Calder\'on commutator defined by $$T_{\Omega,\,a}^*f(x)=\sup_{\epsilon>0}\Big|\int_{|x-y|>\epsilon}\frac{\Omega(x-y)}{|x-y|^{d+1}} \big(a(x)-a(y)\big)f(y)dy\Big|,$$ where $\Omega$ is homogeneous of degree zero, integrable on $S^{d-1}$ and has vanishing moment of order one, $a$ be a function on $\mathbb{R}^d$ such that $\nabla a\in L^{\infty}(\mathbb{R}^d)$. The authors prove that if $\Omega\in L\log L(S^{d-1})$, then $T^*_{\Omega,\,a}$ satisfies an endpoint estimate of $L\log\log L$ type.

math.CA↗

arXiv2023

A bilinear sparse domination for the maximal singular integral operators with rough kernels

Let $\Omega$ be homogeneous of degree zero, integrable on $S^{d-1}$ and have mean value zero, $T_{\Omega}$ be the homogeneous singular integral operator with kernel $\frac{\Omega(x)}{|x|^d}$ and $T_{\Omega}^*$ be the maximal operator associated to $T_{\Omega}$. In this paper, the authors prove that if $\Omega\in L^{\infty}(S^{d-1})$, then for all $r\in (1,\,\infty)$, $T_{\Omega}^*$ enjoys a $(L^\Phi,\,L^r)$ bilinear sparse domination with bound $Cr'\|\Omega\|_{L^{\infty}(S^{d-1})}$, where $\Phi(t)=t\log\log ({\rm e}^2+t)$.

math.CA↗

arXiv2022

$L^p(\mathbb{R}^d)$ boundedness for the Calder\'on commutator with rough kernel

Let $k\in\mathbb{N}$, $\Omega$ be homogeneous of degree zero, integrable on $S^{d-1}$ and have vanishing moment of order $k$, $a$ be a function on $\mathbb{R}^d$ such that $\nabla a\in L^{\infty}(\mathbb{R}^d)$, and $T_{\Omega,\,a;k}$ be the $d$-dimensional Calder\'on commutator defined by $$T_{\Omega,\,a;k}f(x)={\rm p.\,v.}\int_{\mathbb{R}^d}\frac{\Omega(x-y)}{|x-y|^{d+k}}\big(a(x)-a(y)\big)^kf(y){d}y.$$ In this paper, the authors prove that if $$\sup_{\zeta\in S^{d-1}}\int_{S^{d-1}}|\Omega(\theta)|\log ^{\beta} \big(\frac{1}{|\theta\cdot\zeta|}\big)d\theta<\infty,$$ with $\beta\in(1,\,\infty]$, then for $\frac{2\beta}{2\beta-1}<p<2\beta$, $T_{\Omega,\,a;\,k}$ is bounded on $L^p(\mathbb{R}^d)$.

math.CA↗

arXiv2022

On the boundedness of non-standard rough singular integral operators

Let $\Omega$ be homogeneous of degree zero, have vanishing moment of order one on the unit sphere $\mathbb {S}^{d-1}$($d\ge 2$). In this paper, our object of investigation is the following rough non-standard singular integral operator $$T_{\Omega,\,A}f(x)={\rm p.\,v.}\int_{\mathbb{R}^d}\frac{\Omega(x-y)}{|x-y|^{d+1}}\big(A(x)-A(y)-\nabla A(y)(x-y)\big)f(y){\rm d}y,$$ where $A$ is a function defined on $\mathbb{R}^d$ with derivatives of order one in ${\rm BMO}(\mathbb{R}^d)$. We show that $T_{\Omega,\,A}$ enjoys the endpoint $L\log L$ type estimate and is $L^p$ bounded if $\Omega\in L(\log L)^{2}(\mathbb{S}^{d-1})$. These resuts essentially improve the previous known results given by Hofmann for the $L^p$ boundedness of $T_{\Omega,\,A}$ under the condition $\Omega\in L^{q}(\mathbb {S}^{d-1})$ $(q>1)$, Hu and Yang for the endpoint weak $L\log L$ type estimates when $\Omega\in {\rm Lip}_{\alpha}(\mathbb{S}^{d-1})$ for some $\alpha\in (0,\,1]$. Quantitative weighted strong and endpoint weak $L\log L$ type inequalities are proved whenever $\Omega\in L^{\infty}(\mathbb {S}^{d-1})$. The analysis of the weighted results relies heavily on two bilinear sparse dominations of $T_{\Omega,\,A}$ established herein.

math.CA↗

arXiv2021

Improving the Transferability of Adversarial Examples with New Iteration Framework and Input Dropout

Deep neural networks(DNNs) is vulnerable to be attacked by adversarial examples. Black-box attack is the most threatening attack. At present, black-box attack methods mainly adopt gradient-based iterative attack methods, which usually limit the relationship between the iteration step size, the number of iterations, and the maximum perturbation. In this paper, we propose a new gradient iteration framework, which redefines the relationship between the above three. Under this framework, we easily improve the attack success rate of DI-TI-MIM. In addition, we propose a gradient iterative attack method based on input dropout, which can be well combined with our framework. We further propose a multi dropout rate version of this method. Experimental results show that our best method can achieve attack success rate of 96.2\% for defense model on average, which is higher than the state-of-the-art gradient-based attacks.

cs.LG↗

arXiv2021

An endpoint estimate for the commutators of singular integral operators with rough kernels

Let $Ω$ be homogeneous of degree zero and have mean value zero on the unit sphere ${S}^{d-1}$, $T_Ω$ be the homogeneous singular integral operator with kernel $\frac{Ω(x)}{|x|^d}$ and $T_{Ω,\,b}$ be the commutator of $T_Ω$ with symbol $b$. In this paper, we prove that if $Ω\in L(\log L)^2(S^{d-1})$, then for $b\in {\rm BMO}(\mathbb{R}^d)$, $T_{Ω,\,b}$ satisfies an endpoint estimate of $L\log L$ type.

math.CA↗

arXiv2020

Dual-energy CT Reconstruction from Dual Quarter Scans

Compared with conventional single-energy computed tomography (CT), dual-energy CT (DECT) provides better material differentiation but most DECT imaging systems require dual full-angle projection data at different X-ray spectra. Relaxing the requirement of data acquisition is a particularly attractive research to promote the applications of DECT in a wide range of imaging areas. In this work, we design a novel DECT imaging scheme with dual quarter scans and propose an efficient method to reconstruct the desired DECT images from dual limited-angle projection data, which enables DECT on imaging configurations with half-scan and largely reduces scanning angles and radiation doses. We first study the characteristics of image artifacts under dual quarter scans scheme, and find that the directional limited-angle artifacts of DECT images are complementarily distributed in image domain because the corresponding X-rays of high- and low-energy scans are orthogonal. Inspired by this finding, a fusion CT image is generated by integrating the limited-angle DECT images of dual quarter scans. This strategy largely reduces the limited-angle artifacts and preserves the image edges and inner structures. Utilizing the capability of neural network in the modeling of nonlinear problem, a novel Anchor network with single-entry double-out architecture is designed in this work to yield the desired DECT images from the generated fusion CT image. Experimental results on the simulated and real data verify the effectiveness of the proposed method.

physics.med-ph↗

arXiv2020

Dissociable neural representations of adversarially perturbed images in convolutional neural networks and the human brain

Despite the remarkable similarities between convolutional neural networks (CNN) and the human brain, CNNs still fall behind humans in many visual tasks, indicating that there still exist considerable differences between the two systems. Here, we leverage adversarial noise (AN) and adversarial interference (AI) images to quantify the consistency between neural representations and perceptual outcomes in the two systems. Humans can successfully recognize AI images as corresponding categories but perceive AN images as meaningless noise. In contrast, CNNs can correctly recognize AN images but mistakenly classify AI images into wrong categories with surprisingly high confidence. We use functional magnetic resonance imaging to measure brain activity evoked by regular and adversarial images in the human brain, and compare it to the activity of artificial neurons in a prototypical CNN-AlexNet. In the human brain, we find that the representational similarity between regular and adversarial images largely echoes their perceptual similarity in all early visual areas. In AlexNet, however, the neural representations of adversarial images are inconsistent with network outputs in all intermediate processing layers, providing no neural foundations for perceptual similarity. Furthermore, we show that voxel-encoding models trained on regular images can successfully generalize to the neural responses to AI images but not AN images. These remarkable differences between the human brain and AlexNet in the representation-perception relation suggest that future CNNs should emulate both behavior and the internal neural presentations of the human brain.

cs.CV↗

arXiv2020

Weak Type Endpoint Estimates for the Commutators of Rough Singular Integral Operators

Let $Ω$ be homogeneous of degree zero and have mean value zero on the unit sphere ${S}^{n-1}$, $T_Ω$ be the convolution singular integral operator with kernel $\frac{Ω(x)}{|x|^n}$. For $b\in{\rm BMO}(\mathbb{R}^n)$, let $T_{Ω,\,b}$ be the commutator of $T_Ω$. In this paper, by establishing suitable sparse dominations, the authors establish some weak type endpoint estimates of $L\log L$ type for $T_{Ω,\,b}$ when $Ω\in L^q(S^{n-1})$ for some $q\in (1,\,\infty]$.

math.CA↗

arXiv2019

On the composition for rough singular integral operators

In this paper, we investigate the behavior of the bounds of the composition for rough singular integral operators on the weighted space. More precisely, we obtain the quantitative weighted bounds of the composite operator for two singular integral operators with rough homogeneous kernels on $L^p(\mathbb{R}^d,\,w)$, $p\in (1,\,\infty)$, which is smaller than the product of the quantitative weighted bounds for these two rough singular integral operators. Moreover, at the endpoint $p=1$, the $L\log L$ weighted weak type bound is also obtained, which has interests of its own in the theory of rough singular integral even in the unweighted case.

math.CA↗

arXiv2019

A visual encoding model based on deep neural networks and transfer learning

Background: Building visual encoding models to accurately predict visual responses is a central challenge for current vision-based brain-machine interface techniques. To achieve high prediction accuracy on neural signals, visual encoding models should include precise visual features and appropriate prediction algorithms. Most existing visual encoding models employ hand-craft visual features (e.g., Gabor wavelets or semantic labels) or data-driven features (e.g., features extracted from deep neural networks (DNN)). They also assume a linear mapping between feature representation to brain activity. However, it remains unknown whether such linear mapping is sufficient for maximizing prediction accuracy. New Method: We construct a new visual encoding framework to predict cortical responses in a benchmark functional magnetic resonance imaging (fMRI) dataset. In this framework, we employ the transfer learning technique to incorporate a pre-trained DNN (i.e., AlexNet) and train a nonlinear mapping from visual features to brain activity. This nonlinear mapping replaces the conventional linear mapping and is supposed to improve prediction accuracy on brain activity. Results: The proposed framework can significantly predict responses of over 20% voxels in early visual areas (i.e., V1-lateral occipital region, LO) and achieve unprecedented prediction accuracy. Comparison with Existing Methods: Comparing to two conventional visual encoding models, we find that the proposed encoding model shows consistent higher prediction accuracy in all early visual areas, especially in relatively anterior visual areas (i.e., V4 and LO). Conclusions: Our work proposes a new framework to utilize pre-trained visual features and train non-linear mappings from visual features to brain activity.

cs.CV↗

arXiv2018

Weighted weak type endpoint estimates for the composition of Calderon-Zygmund operators

Let $T_1$, $T_2$ be two Calderón-Zygmund operators and $T_{1,\,b}$ be the commutator of $T_1$ with symbol $b\in {\rm BMO}(\mathbb{R}^n)$. In this paper, the author prove that, the composite operator $T_1T_2$ satisfies the following estimate: for $λ>0$ and weight $w\in A_1(\mathbb{R}^n)$, \begin{eqnarray*}&&w\big(\{x\in\mathbb{R}^n:\,|T_{1} T_2f(x)|>λ\}\big)\\ &&\quad\lesssim [w]_{A_1}[w]_{A_{\infty}}\log ({\rm e}+[w]_{A_{\infty}}\big) \int_{\mathbb{R}^n}\frac{|f(x)|}λ\log \Big({\rm e}+\frac{|f(x)|}λ\Big)w(x)dx,\nonumber \end{eqnarray*} and the composite operator $T_{1,b}T_2$ satisfies that \begin{eqnarray*}&&w\big(\{x\in\mathbb{R}^n:\,|T_{1,b} T_2f(x)|>λ\}\big)\\ &&\quad\lesssim [w]_{A_1}[w]_{A_{\infty}}\log^2 ({\rm e}+[w]_{A_{\infty}}\big) \int_{\mathbb{R}^n}\frac{|f(x)|}λ\log^2 \Big({\rm e}+\frac{|f(x)|}λ\Big)w(x)dx. \end{eqnarray*}

math.CA↗

arXiv2018

The composition of singular integral operators with nonsmooth kernels

Let $T_1$, $T_2$ be two singular integral operators with nonsmooth kernels introduced by Duong and McIntosh. In this paper, by establishing certain bi-sublinear sparse domination, the authors obtain some quantitative bounds on $L^p(\mathbb{R}^n,\,w)$ with $p\in(1,\,\infty)$ and $w\in A_p(\mathbb{R}^n)$ for the composite operator $T_1T_2$. Some weighted weak type endpoint estimates are also given.

math.CA↗

arXiv2018

Weighted estimates for the Calderón commutator

In this paper, the authors establish some weighted estimates for the Calderón commutator defined by \begin{eqnarray*} &&\mathcal{C}_{m+1,\,A}(a_1,\dots,a_{m};f)(x) &&\quad={\rm p.\,v.}\,\int_{\mathbb{R}}\frac{P_2(A;\,x,\,y)\prod_{j=1}^m(A_j(x)-A_j(y))}{(x-y)^{m+2}}f(y){\rm d}y, \end{eqnarray*} with $P_2(A;\,x,\,y)=A(x)-A(y)-A'(y)(x-y)$. Dominating this operator by multi(sub)linear sparse operators, the authors establish the weighted bounds from $L^{p_1}(\mathbb{R},w_1)$ $\times\dots\times L^{p_m}(\mathbb{R},w_m)$ to $L^{p}(\mathbb{R},ν_{\vec{w}})$, with $p_1,\dots,p_m \in (1,\,\infty)$, $1/p=1/p_1+\dots+1/p_m$, and $\vec{w}=(w_1,\,\dots,\,w_m)\in A_{\vec{P}}(\mathbb{R}^{m+1})$. The authors also obtain the weighted weak type endpoint estimates for this operator

math.CA↗

arXiv2018

Weighted complete continuity for the commutator of Marcinkiewicz integral

Let $Ω$ be homogeneous of degree zero, have mean value zero and integrable on the unit sphere, and $\mathcal{M}_Ω$ be the higher-dimensional Marcinkiewicz integral associated with $Ω$. In this paper, the author considers the complete continuity on weighted $L^p(\mathbb{R}^n)$ spaces with $A_p(\mathbb{R}^n)$ weights, weighted Morrey spaces with $A_p(\mathbb{R}^n)$ weights, for the commutator generated by ${\rm CMO}(\mathbb{R}^n)$ functions and $\mathcal{M}_Ω$ when $Ω$ satisfies certain size conditions.

math.CA↗

arXiv2017

Weighted vector-valued estimates for a non-standard Calderón-Zygmund operator

In this paper, the author considers the weighted vector-valued estimate for the operator defined by $$T_Af(x)={\rm p.\,v.}\int_{\mathbb{R}^n}\frac{Ω(x-y)}{|x-y|^{n+1}}\big(A(x)-A(y)-\nabla A(y)\big)f(y){\rm d}y,$$ and the corresponding maximal operator $T_A^*$, where $Ω$ is homogeneous of degree zero, has vanishing moment of order one, $A$ is a function in $\mathbb{R}^n$ such that $\nabla A\in {\rm BMO}(\mathbb{R}^n)$. By a pointwise estimate for $\|\{T_Af_k(x)\}\|_{l^q}$ and the weighted $L^p$ estimates for the sparse operator $$\mathcal{A}_{\mathcal{S},\,L(\log L)^β}f(x)=\sum_{Q\in\mathcal{S}}\|f\|_{L(\log L)^β,\,Q}χ_{Q}(x) ,$$ the author establishes some weak and endpoint quantitative weighted vector-valued estimates for $T_A$ and $T_A^*$.

math.CA↗

arXiv2016

Weighted vector-valued bounds for the singular integral operators with nonsmooth kernels

Let $T$ be a singular integral operator with non-smooth kernel which were introduced by Duong and McIntosh. In this paper, we prove that this operator and its corresponding grand maximal operator satisfies certain weak type endpoint vector-valued estimate of $L\log L$ type. As an application we established a refined weighted vector-valued bound for this operator.

math.CA↗

arXiv2016

Efficient Image Reconstruction and Practical Decomposition for Dual-energy Computed Tomography

Dual-energy computed tomography (DECT) has shown great potential and promising applications in advanced imaging fields for its capabilities of material decomposition. However, image reconstructions and decompositions under sparse views dataset suffers severely from multi factors, such as insufficiencies of data, appearances of noise, and inconsistencies of observations. Under sparse views, conventional filtered back-projection type reconstruction methods fails to provide CT images with satisfying quality. Moreover, direct image decomposition is unstable and meet with noise boost even with full views dataset. This paper proposes an iterative image reconstruction algorithm and a practical image domain decomposition method for DECT. On one hand, the reconstruction algorithm is formulated as an optimization problem, which containing total variation regularization term and data fidelity term. The alternating direction method is utilized to design the corresponding algorithm which shows faster convergence speed compared with the existing ones. On the other hand, the image domain decomposition applies the penalized least square (PLS) estimation on decomposing the material mappings. The PLS includes linear combination term and the regularization term which enforces the smoothness on estimation images. The authors implement and evaluate the proposed joint method on real DECT projections and compare the method with typical and state-of-the-art reconstruction and decomposition methods. The experiments on dataset of an anthropomorphic head phantom show that our methods have advantages on noise suppression and edge reservation, without blurring the fine structures in the sinus area in the phantom. Compared to the existing approaches, our method achieves a superior performance on DECT imaging with respect to reconstruction accuracy and decomposition quality.

physics.med-ph↗