arXiv subjects

Thomas Yu

Publications and source records attributed to Thomas Yu.

15 recordsLinked to original sources

arXiv2024

Isoperimetric Ratios of Toroidal Dupin Cyclides

The combination of recent results due to Yu and Chen [Proc. AMS 150(4), 2020, 1749-1765] and to Bostan and Yurkevich [Proc. AMS 150(5), 2022, 2131-2136] shows that the 3-D Euclidean shape of the square Clifford torus is uniquely determined by its isoperimetric ratio. This solves part of the still open uniqueness problem of the Canham model for biomembranes. In this work we investigate the generalization of the aforementioned result to the case of a rectangular Clifford torus. Like the square case, we find closed-form formulas in terms of hypergeometric functions for the isoperimetric ratio of its stereographic projection to $\mathbb{R}^3$ and show that the corresponding function is strictly increasing. But unlike the square case, we show that the isoperimetric ratio does not uniquely determine the Euclidean shape of a rectangular Clifford torus.

math.DG↗

arXiv2023

The Essential Best and Average Rate of Convergence of the Exact Line Search Gradient Descent Method

It is very well known that when the exact line search gradient descent method is applied to a convex quadratic objective, the worst-case rate of convergence (ROC), among all seed vectors, deteriorates as the condition number of the Hessian of the objective grows. By an elegant analysis due to H. Akaike, it is generally believed -- but not proved -- that in the ill-conditioned regime the ROC for almost all initial vectors, and hence also the average ROC, is close to the worst case ROC. We complete Akaike's analysis by determining the \emph{essential best case ROC} (defined in a measure-theoretic way) by using a dynamical system approach, facilitated by the theorem of center and stable manifolds. Our analysis also makes apparent the effect of an intermediate eigenvalue in the Hessian by establishing the following amusing result: In the absence of an intermediate eigenvalue, the average ROC gets arbitrarily \emph{fast} -- not slow -- as the Hessian gets increasingly ill-conditioned. We discuss in passing some contemporary applications of exact line search GD to well-conditioned polynomial optimization problems arising from imaging and data sciences. In particular, we observe that a tailored exact line search GD algorithm for a POP arising from the phase retrieval problem is only 50\% more expensive per iteration than its constant step size counterpart, while promising a ROC only matched by the optimally tuned (constant) step size which can rarely be achieved in practice.

math.NA↗

arXiv2023

The Brain Tumor Segmentation (BraTS) Challenge 2023: Brain MR Image Synthesis for Tumor Segmentation (BraSyn)

Automated brain tumor segmentation methods have become well-established and reached performance levels offering clear clinical utility. These methods typically rely on four input magnetic resonance imaging (MRI) modalities: T1-weighted images with and without contrast enhancement, T2-weighted images, and FLAIR images. However, some sequences are often missing in clinical practice due to time constraints or image artifacts, such as patient motion. Consequently, the ability to substitute missing modalities and gain segmentation performance is highly desirable and necessary for the broader adoption of these algorithms in the clinical routine. In this work, we present the establishment of the Brain MR Image Synthesis Benchmark (BraSyn) in conjunction with the Medical Image Computing and Computer-Assisted Intervention (MICCAI) 2023. The primary objective of this challenge is to evaluate image synthesis methods that can realistically generate missing MRI modalities when multiple available images are provided. The ultimate aim is to facilitate automated brain tumor segmentation pipelines. The image dataset used in the benchmark is diverse and multi-modal, created through collaboration with various hospitals and research institutions.

eess.IV↗

arXiv2022

Slice estimation in diffusion MRI of neonatal and fetal brains in image and spherical harmonics domains using autoencoders

Diffusion MRI (dMRI) of the developing brain can provide valuable insights into the white matter development. However, slice thickness in fetal dMRI is typically high (i.e., 3-5 mm) to freeze the in-plane motion, which reduces the sensitivity of the dMRI signal to the underlying anatomy. In this study, we aim at overcoming this problem by using autoencoders to learn unsupervised efficient representations of brain slices in a latent space, using raw dMRI signals and their spherical harmonics (SH) representation. We first learn and quantitatively validate the autoencoders on the developing Human Connectome Project pre-term newborn data, and further test the method on fetal data. Our results show that the autoencoder in the signal domain better synthesized the raw signal. Interestingly, the fractional anisotropy and, to a lesser extent, the mean diffusivity, are best recovered in missing slices by using the autoencoder trained with SH coefficients. A comparison was performed with the same maps reconstructed using an autoencoder trained with raw signals, as well as conventional interpolation methods of raw signals and SH coefficients. From these results, we conclude that the recovery of missing/corrupted slices should be performed in the signal domain if the raw signal is aimed to be recovered, and in the SH domain if diffusion tensor properties (i.e., fractional anisotropy) are targeted. Notably, the trained autoencoders were able to generalize to fetal dMRI data acquired using a much smaller number of diffusion gradients and a lower b-value, where we qualitatively show the consistency of the estimated diffusion tensor maps.

eess.IV↗

arXiv2022

The NLP Sandbox: an efficient model-to-data system to enable federated and unbiased evaluation of clinical NLP models

Objective The evaluation of natural language processing (NLP) models for clinical text de-identification relies on the availability of clinical notes, which is often restricted due to privacy concerns. The NLP Sandbox is an approach for alleviating the lack of data and evaluation frameworks for NLP models by adopting a federated, model-to-data approach. This enables unbiased federated model evaluation without the need for sharing sensitive data from multiple institutions. Materials and Methods We leveraged the Synapse collaborative framework, containerization software, and OpenAPI generator to build the NLP Sandbox (nlpsandbox.io). We evaluated two state-of-the-art NLP de-identification focused annotation models, Philter and NeuroNER, using data from three institutions. We further validated model performance using data from an external validation site. Results We demonstrated the usefulness of the NLP Sandbox through de-identification clinical model evaluation. The external developer was able to incorporate their model into the NLP Sandbox template and provide user experience feedback. Discussion We demonstrated the feasibility of using the NLP Sandbox to conduct a multi-site evaluation of clinical text de-identification models without the sharing of data. Standardized model and data schemas enable smooth model transfer and implementation. To generalize the NLP Sandbox, work is required on the part of data owners and model developers to develop suitable and standardized schemas and to adapt their data or model to fit the schemas. Conclusions The NLP Sandbox lowers the barrier to utilizing clinical data for NLP model evaluation and facilitates federated, multi-site, unbiased evaluation of NLP models.

cs.CL↗

arXiv2022

Validation and Generalizability of Self-Supervised Image Reconstruction Methods for Undersampled MRI

Deep learning methods have become the state of the art for undersampled MR reconstruction. Particularly for cases where it is infeasible or impossible for ground truth, fully sampled data to be acquired, self-supervised machine learning methods for reconstruction are becoming increasingly used. However potential issues in the validation of such methods, as well as their generalizability, remain underexplored. In this paper, we investigate important aspects of the validation of self-supervised algorithms for reconstruction of undersampled MR images: quantitative evaluation of prospective reconstructions, potential differences between prospective and retrospective reconstructions, suitability of commonly used quantitative metrics, and generalizability. Two self-supervised algorithms based on self-supervised denoising and the deep image prior were investigated. These methods are compared to a least squares fitting and a compressed sensing reconstruction using in-vivo and phantom data. Their generalizability was tested with prospectively under-sampled data from experimental conditions different to the training. We show that prospective reconstructions can exhibit significant distortion relative to retrospective reconstructions/ground truth. Furthermore, pixel-wise quantitative metrics may not capture differences in perceptual quality accurately, in contrast to a perceptual metric. In addition, all methods showed potential for generalization; however, generalizability is more affected by changes in anatomy/contrast than other changes. We further showed that no-reference image metrics correspond well with human rating of image quality for studying generalizability. Finally, we showed that a well-tuned compressed sensing reconstruction and learned denoising perform similarly on all data.

eess.IV↗

arXiv2021

FaBiAN: A Fetal Brain magnetic resonance Acquisition Numerical phantom

Accurate characterization of in utero human brain maturation is critical as it involves complex and interconnected structural and functional processes that may influence health later in life. Magnetic resonance imaging is a powerful tool to investigate equivocal neurological patterns during fetal development. However, the number of acquisitions of satisfactory quality available in this cohort of sensitive subjects remains scarce, thus hindering the validation of advanced image processing techniques. Numerical phantoms can mitigate these limitations by providing a controlled environment with a known ground truth. In this work, we present FaBiAN, an open-source Fetal Brain magnetic resonance Acquisition Numerical phantom that simulates clinical T2-weighted fast spin echo sequences of the fetal brain. This unique tool is based on a general, flexible and realistic setup that includes stochastic fetal movements, thus providing images of the fetal brain throughout maturation comparable to clinical acquisitions. We demonstrate its value to evaluate the robustness and optimize the accuracy of an algorithm for super-resolution fetal brain magnetic resonance imaging from simulated motion-corrupted 2D low-resolution series as compared to a synthetic high-resolution reference volume. We also show that the images generated can complement clinical datasets to support data-intensive deep learning methods for fetal brain tissue segmentation.

physics.med-ph↗

arXiv2021

The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification

The BraTS 2021 challenge celebrates its 10th anniversary and is jointly organized by the Radiological Society of North America (RSNA), the American Society of Neuroradiology (ASNR), and the Medical Image Computing and Computer Assisted Interventions (MICCAI) society. Since its inception, BraTS has been focusing on being a common benchmarking venue for brain glioma segmentation algorithms, with well-curated multi-institutional multi-parametric magnetic resonance imaging (mpMRI) data. Gliomas are the most common primary malignancies of the central nervous system, with varying degrees of aggressiveness and prognosis. The RSNA-ASNR-MICCAI BraTS 2021 challenge targets the evaluation of computational algorithms assessing the same tumor compartmentalization, as well as the underlying tumor's molecular characterization, in pre-operative baseline mpMRI data from 2,040 patients. Specifically, the two tasks that BraTS 2021 focuses on are: a) the segmentation of the histologically distinct brain tumor sub-regions, and b) the classification of the tumor's O[6]-methylguanine-DNA methyltransferase (MGMT) promoter methylation status. The performance evaluation of all participating algorithms in BraTS 2021 will be conducted through the Sage Bionetworks Synapse platform (Task 1) and Kaggle (Task 2), concluding in distributing to the top ranked participants monetary awards of $60,000 collectively.

cs.CV↗

arXiv2021

Test-Time Adaptation for Super-Resolution: You Only Need to Overfit on a Few More Images

Existing reference (RF)-based super-resolution (SR) models try to improve perceptual quality in SR under the assumption of the availability of high-resolution RF images paired with low-resolution (LR) inputs at testing. As the RF images should be similar in terms of content, colors, contrast, etc. to the test image, this hinders the applicability in a real scenario. Other approaches to increase the perceptual quality of images, including perceptual loss and adversarial losses, tend to dramatically decrease fidelity to the ground-truth through significant decreases in PSNR/SSIM. Addressing both issues, we propose a simple yet universal approach to improve the perceptual quality of the HR prediction from a pre-trained SR network on a given LR input by further fine-tuning the SR network on a subset of images from the training dataset with similar patterns of activation as the initial HR prediction, with respect to the filters of a feature extractor. In particular, we show the effects of fine-tuning on these images in terms of the perceptual quality and PSNR/SSIM values. Contrary to perceptually driven approaches, we demonstrate that the fine-tuned network produces a HR prediction with both greater perceptual quality and minimal changes to the PSNR/SSIM with respect to the initial HR prediction. Further, we present novel numerical experiments concerning the filters of SR networks, where we show through filter correlation, that the filters of the fine-tuned network from our method are closer to "ideal" filters, than those of the baseline network or a network fine-tuned on random images.

cs.CV↗

arXiv2020

T2 Mapping from Super-Resolution-Reconstructed Clinical Fast Spin Echo Magnetic Resonance Acquisitions

Relaxometry studies in preterm and at-term newborns have provided insight into brain microstructure, thus opening new avenues for studying normal brain development and supporting diagnosis in equivocal neurological situations. However, such quantitative techniques require long acquisition times and therefore cannot be straightforwardly translated to in utero brain developmental studies. In clinical fetal brain magnetic resonance imaging routine, 2D low-resolution T2-weighted fast spin echo sequences are used to minimize the effects of unpredictable fetal motion during acquisition. As super-resolution techniques make it possible to reconstruct a 3D high-resolution volume of the fetal brain from clinical low-resolution images, their combination with quantitative acquisition schemes could provide fast and accurate T2 measurements. In this context, the present work demonstrates the feasibility of using super-resolution reconstruction from conventional T2-weighted fast spin echo sequences for 3D isotropic T2 mapping. A quantitative magnetic resonance phantom was imaged using a clinical T2-weighted fast spin echo sequence at variable echo time to allow for super-resolution reconstruction at every echo time and subsequent T2 mapping of samples whose relaxometric properties are close to those of fetal brain tissue. We demonstrate that this approach is highly repeatable, accurate and robust when using six echo times (total acquisition time under 9 minutes) as compared to gold-standard single-echo spin echo sequences (several hours for one single 2D slice).

eess.IV↗

arXiv2020

Model-Informed Machine Learning for Multi-component T2 Relaxometry

Recovering the T2 distribution from multi-echo T2 magnetic resonance (MR) signals is challenging but has high potential as it provides biomarkers characterizing the tissue micro-structure, such as the myelin water fraction (MWF). In this work, we propose to combine machine learning and aspects of parametric (fitting from the MRI signal using biophysical models) and non-parametric (model-free fitting of the T2 distribution from the signal) approaches to T2 relaxometry in brain tissue by using a multi-layer perceptron (MLP) for the distribution reconstruction. For training our network, we construct an extensive synthetic dataset derived from biophysical models in order to constrain the outputs with \textit{a priori} knowledge of \textit{in vivo} distributions. The proposed approach, called Model-Informed Machine Learning (MIML), takes as input the MR signal and directly outputs the associated T2 distribution. We evaluate MIML in comparison to non-parametric and parametric approaches on synthetic data, an ex vivo scan, and high-resolution scans of healthy subjects and a subject with Multiple Sclerosis. In synthetic data, MIML provides more accurate and noise-robust distributions. In real data, MWF maps derived from MIML exhibit the greatest conformity to anatomical scans, have the highest correlation to a histological map of myelin volume, and the best unambiguous lesion visualization and localization, with superior contrast between lesions and normal appearing tissue. In whole-brain analysis, MIML is 22 to 4980 times faster than non-parametric and parametric methods, respectively.

physics.med-ph↗

arXiv2020

Benefiting from Bicubically Down-Sampled Images for Learning Real-World Image Super-Resolution

Super-resolution (SR) has traditionally been based on pairs of high-resolution images (HR) and their low-resolution (LR) counterparts obtained artificially with bicubic downsampling. However, in real-world SR, there is a large variety of realistic image degradations and analytically modeling these realistic degradations can prove quite difficult. In this work, we propose to handle real-world SR by splitting this ill-posed problem into two comparatively more well-posed steps. First, we train a network to transform real LR images to the space of bicubically downsampled images in a supervised manner, by using both real LR/HR pairs and synthetic pairs. Second, we take a generic SR network trained on bicubically downsampled images to super-resolve the transformed LR image. The first step of the pipeline addresses the problem by registering the large variety of degraded images to a common, well understood space of images. The second step then leverages the already impressive performance of SR on bicubically downsampled images, sidestepping the issues of end-to-end training on datasets with many different image degradations. We demonstrate the effectiveness of our proposed method by comparing it to recent methods in real-world SR and show that our proposed approach outperforms the state-of-the-art works in terms of both qualitative and quantitative results, as well as results of an extensive user study conducted on several real image datasets.

eess.IV↗

arXiv2020

On the Uniqueness of Clifford Torus with Prescribed Isoperimetric Ratio

The Marques-Neves theorem asserts that among all the torodial (i.e. genus 1) closed surfaces, the Clifford torus has the minimal Willmore energy $\int H^2 \, dA$. % It is a natural conjecture that if one prescribes the isoperimetric Since the Willmore energy is invariant M{\"o}bius transformations, it can be shown that there is a one-parameter family, up to homotheties, of genus 1 Willmore minimizers. It is then a natural conjecture that such a minimizer is unique if one prescribes its isoperimetric ratio. In this article, we show that this conjecture can be reduced to the positivity question of a polynomial recurrence.

math.DG↗

arXiv2019

Numerical Methods for Biomembranes: conforming subdivision methods versus non-conforming PL methods

The Canham-Helfrich-Evans models of biomembranes consist of a family of geometric constrained variational problems. In this article, we compare two classes of numerical methods for these variational problems based on piecewise linear (PL) and subdivision surfaces (SS). Since SS methods are based on spline approximation and can be viewed as higher order versions of PL methods, one may expect that the only difference between the two methods is in the accuracy order. In this paper, we prove that a numerical method based on minimizing any one of the `PL Willmore energies' proposed in the literature would fail to converge to a solution of the continuous problem, whereas a method based on minimization of the bona fide Willmore energy, well-defined for SS but not PL surfaces, succeeds. Motivated by this analysis, we propose also a regularization method for the PL method based on techniques from conformal geometry. We address a number of implementation issues crucial for the efficiency of our solver. A software package called Wmincon accompanies this article, provides parallel implementations of all the relevant geometric functionals. When combined with a standard constrained optimization solver, the geometric variational problems can then be solved numerically. To this end, we realize that some of the available optimization algorithms/solvers are capable of preserving symmetry, while others manage to break symmetry; we explore the consequences of this observation.

math.NA↗

arXiv2016

Reducing overfitting in challenge-based competitions

Over-fitting is a dreaded foe in challenge-based competitions. Because participants rely on public leaderboards to evaluate and refine their models, there is always the danger they might over-fit to the holdout data supporting the leaderboard. The recently published Ladder algorithm aims to address this problem by preventing the participants from exploiting willingly or inadvertently minor fluctuations in public leaderboard scores during model refinement. In this paper, we report a vulnerability of the Ladder that induces severe over-fitting of the leaderboard when the sample size is small. To circumvent this attack, we propose a variation of the Ladder that releases a bootstrapped estimate of the public leaderboard score instead of providing participants with a direct measure of performance. We also extend the scope of the Ladder to arbitrary performance metrics by relying on a more broadly applicable testing procedure based on the Bayesian bootstrap. Our method makes it possible to use a leaderboard, with the technical and social advantages that it provides, even in cases where data is scant.

stat.AP↗