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Cheng Ouyang

Publications and source records attributed to Cheng Ouyang.

At least 73 records · Page 4Linked to original sources
arXiv2019

Unsupervised Multi-modal Style Transfer for Cardiac MR Segmentation

In this work, we present a fully automatic method to segment cardiac structures from late-gadolinium enhanced (LGE) images without using labelled LGE data for training, but instead by transferring the anatomical knowledge and features learned on annotated balanced steady-state free precession (bSSFP) images, which are easier to acquire. Our framework mainly consists of two neural networks: a multi-modal image translation network for style transfer and a cascaded segmentation network for image segmentation. The multi-modal image translation network generates realistic and diverse synthetic LGE images conditioned on a single annotated bSSFP image, forming a synthetic LGE training set. This set is then utilized to fine-tune the segmentation network pre-trained on labelled bSSFP images, achieving the goal of unsupervised LGE image segmentation. In particular, the proposed cascaded segmentation network is able to produce accurate segmentation by taking both shape prior and image appearance into account, achieving an average Dice score of 0.92 for the left ventricle, 0.83 for the myocardium, and 0.88 for the right ventricle on the test set.

eess.IV↗
arXiv2019

Data consistency networks for (calibration-less) accelerated parallel MR image reconstruction

We present simple reconstruction networks for multi-coil data by extending deep cascade of CNN's and exploiting the data consistency layer. In particular, we propose two variants, where one is inspired by POCSENSE and the other is calibration-less. We show that the proposed approaches are competitive relative to the state of the art both quantitatively and qualitatively.

eess.IV↗
arXiv2019

Data Efficient Unsupervised Domain Adaptation for Cross-Modality Image Segmentation

Deep learning models trained on medical images from a source domain (e.g. imaging modality) often fail when deployed on images from a different target domain, despite imaging common anatomical structures. Deep unsupervised domain adaptation (UDA) aims to improve the performance of a deep neural network model on a target domain, using solely unlabelled target domain data and labelled source domain data. However, current state-of-the-art methods exhibit reduced performance when target data is scarce. In this work, we introduce a new data efficient UDA method for multi-domain medical image segmentation. The proposed method combines a novel VAE-based feature prior matching, which is data-efficient, and domain adversarial training to learn a shared domain-invariant latent space which is exploited during segmentation. Our method is evaluated on a public multi-modality cardiac image segmentation dataset by adapting from the labelled source domain (3D MRI) to the unlabelled target domain (3D CT). We show that by using only one single unlabelled 3D CT scan, the proposed architecture outperforms the state-of-the-art in the same setting. Finally, we perform ablation studies on prior matching and domain adversarial training to shed light on the theoretical grounding of the proposed method.

eess.IV↗
arXiv2019

VS-Net: Variable splitting network for accelerated parallel MRI reconstruction

In this work, we propose a deep learning approach for parallel magnetic resonance imaging (MRI) reconstruction, termed a variable splitting network (VS-Net), for an efficient, high-quality reconstruction of undersampled multi-coil MR data. We formulate the generalized parallel compressed sensing reconstruction as an energy minimization problem, for which a variable splitting optimization method is derived. Based on this formulation we propose a novel, end-to-end trainable deep neural network architecture by unrolling the resulting iterative process of such variable splitting scheme. VS-Net is evaluated on complex valued multi-coil knee images for 4-fold and 6-fold acceleration factors. We show that VS-Net outperforms state-of-the-art deep learning reconstruction algorithms, in terms of reconstruction accuracy and perceptual quality. Our code is publicly available at https://github.com/j-duan/VS-Net.

eess.IV↗
arXiv2019

Precise Local Estimates for Hypoelliptic Differential Equations driven by Fractional Brownian Motions

This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a uniform hypoellipticity condition, we establish a sharp local estimate on the associated control distance function and a sharp local lower estimate on the density of the solution. Our methodology relies heavily on the rough paths structure of the equation.

math.PR↗
arXiv2019

Density of the signature process of fBm

We study the density of the signature of fractional Brownian motions with parameter $H>1/4$. In particular, we prove existence, smoothness, global Gaussian upper bounds and Varadhan's type asymptotics for this density. A key result is that the estimates on the density we obtain are controlled by the Carnot-Carathéodory distance of the group.

math.PR↗
arXiv2018

PnP-AdaNet: Plug-and-Play Adversarial Domain Adaptation Network with a Benchmark at Cross-modality Cardiac Segmentation

Deep convolutional networks have demonstrated the state-of-the-art performance on various medical image computing tasks. Leveraging images from different modalities for the same analysis task holds clinical benefits. However, the generalization capability of deep models on test data with different distributions remain as a major challenge. In this paper, we propose the PnPAdaNet (plug-and-play adversarial domain adaptation network) for adapting segmentation networks between different modalities of medical images, e.g., MRI and CT. We propose to tackle the significant domain shift by aligning the feature spaces of source and target domains in an unsupervised manner. Specifically, a domain adaptation module flexibly replaces the early encoder layers of the source network, and the higher layers are shared between domains. With adversarial learning, we build two discriminators whose inputs are respectively multi-level features and predicted segmentation masks. We have validated our domain adaptation method on cardiac structure segmentation in unpaired MRI and CT. The experimental results with comprehensive ablation studies demonstrate the excellent efficacy of our proposed PnP-AdaNet. Moreover, we introduce a novel benchmark on the cardiac dataset for the task of unsupervised cross-modality domain adaptation. We will make our code and database publicly available, aiming to promote future studies on this challenging yet important research topic in medical imaging.

cs.CV↗
arXiv2018

Unsupervised Cross-Modality Domain Adaptation of ConvNets for Biomedical Image Segmentations with Adversarial Loss

Convolutional networks (ConvNets) have achieved great successes in various challenging vision tasks. However, the performance of ConvNets would degrade when encountering the domain shift. The domain adaptation is more significant while challenging in the field of biomedical image analysis, where cross-modality data have largely different distributions. Given that annotating the medical data is especially expensive, the supervised transfer learning approaches are not quite optimal. In this paper, we propose an unsupervised domain adaptation framework with adversarial learning for cross-modality biomedical image segmentations. Specifically, our model is based on a dilated fully convolutional network for pixel-wise prediction. Moreover, we build a plug-and-play domain adaptation module (DAM) to map the target input to features which are aligned with source domain feature space. A domain critic module (DCM) is set up for discriminating the feature space of both domains. We optimize the DAM and DCM via an adversarial loss without using any target domain label. Our proposed method is validated by adapting a ConvNet trained with MRI images to unpaired CT data for cardiac structures segmentations, and achieved very promising results.

cs.CV↗
arXiv2017

Efficient posterior inference on the volatility of a jump diffusion process

Jump diffusion processes are widely used to model asset prices over time, mainly for their ability to capture complex discontinuous behavior, but inference on the model parameters remains a challenge. Here our goal is posterior inference on the volatility coefficient of the diffusion part of the process based on discrete samples. A Bayesian approach requires specification of a model for the jump part of the process, prior distributions for the corresponding parameters, and computation of the joint posterior. Since the volatility coefficient is our only interest, it would be desirable to avoid the modeling and computational costs associated with the jump part of the process. Towards this, we consider a {\em purposely misspecified model} that ignores the jump part entirely. We work out precisely the asymptotic behavior of the Bayesian posterior under the misspecified model, propose some simple modifications to correct for the effects of misspecification, and demonstrate that our modified posterior inference on the volatility is efficient in the sense that its asymptotic variance equals the no-jumps model Cramér--Rao bound.

stat.ME↗
arXiv2016

On the law of the iterated logarithm for Brownian motion on compact manifolds

By taking a functional analytic point of view, we consider a family of distributions (continuous linear functionals on smooth functions), denoted by $\{μ_t,t>0\}$, associated to the law of iterated logarithm for Brownian motion on a compact manifold. We give a complete characterization of the collection of limiting distributions of $\{μ_t, t>0\}$.

math.PR↗
arXiv2016

Local times of stochastic differential equations driven by fractional Brownian motions

In this paper, we study the existence and (Hölder) regularity of local times of stochastic differential equations driven by fractional Brownian motions. In particular, we show that in one dimension and in the rough case H<1/2, the Hölder exponent (in t) of the local time is 1-H, where H is the Hurst parameter of the driving fractional Brownian motion.

math.PR↗
arXiv2015

Fractal Dimensions of Rough Differential Equations Driven by Fractional Brownian Motions

In this work we study fractal properties of rough differential equations driven by a fractional Brownian motions with Hurst parameter $H>\frac{1}{4}$. In particular, we show that the Hausdorff dimension of the sample paths of the solution is $\min\{d,\frac{1}{H}\}$ and that the Hausdorff dimension of the level set $L_x=\{ t\in[ε,1]: X_t=x\}$ is $1-dH$ with positive probability when $d<\frac{1}{H}$

math.PR↗
arXiv2014

Small-time expansions for local jump-diffusion models with infinite jump activity

We consider a Markov process $X$, which is the solution of a stochastic differential equation driven by a Lévy process $Z$ and an independent Wiener process $W$. Under some regularity conditions, including non-degeneracy of the diffusive and jump components of the process as well as smoothness of the Lévy density of $Z$ outside any neighborhood of the origin, we obtain a small-time second-order polynomial expansion for the tail distribution and the transition density of the process $X$. Our method of proof combines a recent regularizing technique for deriving the analog small-time expansions for a Lévy process with some new tail and density estimates for jump-diffusion processes with small jumps based on the theory of Malliavin calculus, flow of diffeomorphisms for SDEs, and time-reversibility. As an application, the leading term for out-of-the-money option prices in short maturity under a local jump-diffusion model is also derived.

math.PR↗
arXiv2014

On probability laws of solutions to differential systems driven by a fractional Brownian motion

This article investigates several properties related to densities of solutions X to differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4. We first determine conditions for strict positivity of the density of X_t. Then we obtain some exponential bounds for this density when the diffusion coefficient satisfies an elliptic type condition. Finally, still in the elliptic case, we derive some bounds on the hitting probabilities of sets by fractional differential systems in terms of Newtonian capacities.

math.PR↗
arXiv2013

Smoothing effect of rough differential equations driven by fractional Brownian motions

In this work we study the smoothing effect of rough differential equations driven by a fractional Brownian motion with parameter $H>1/4$. The regularization estimates we obtain generalize to the fractional Brownian motion previous results by Kusuoka and Stroock and can be seen as a quantitative version of the existence of smooth densities under Hörmander's type conditions.

math.PR↗
arXiv2011

Upper bounds for the density of solutions of stochastic differential equations driven by fractional Brownian motions

In this paper we study upper bounds for the density of solution of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/3. We show that under some geometric conditions, in the regular case H > 1/2, the density of the solution satisfy the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough case H > 1/3 and under the same geometric conditions, we show that the density of the solution is smooth and admits an upper sub-Gaussian bound.

math.PR↗