CRII:CIF: Towards A Manifold-based Framework for the Brain-Computer Interface

CRII:CIF：迈向基于流形的脑机接口框架

• 批准号: 2153492
• 负责人: Jingyi Zheng
• 金额: $ 17.5万
• 依托单位: Auburn University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-05-01 至 2025-04-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2153492&HistoricalAwards=false
• 关键词: CRII; CIF; Towards; Manifold; based

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).A brain-computer interface (BCI) is a computer-based system that builds communication pathways between the human brain and external devices. A BCI acquires brain signals and translates them into commands for the external device(s) to perform actions intended by the user. BCIs have shown great potential for helping people with severe motor impairments, detecting and diagnosing health issues, and providing new interfaces for applications such as gaming. Numerous methods have been used to process BCI data, which are mostly spatial and temporal in nature, e.g., multi-channel electroencephalography and functional magnetic resonance imaging. Unfortunately, existing techniques still suffer from low robustness and low reliability due to sensitivity to artifacts, noise and outliers, and require lengthy calibration. These challenges will be addressed by developing a novel framework which efficiently and robustly models the covariance matrices associated with the spatial and temporal patterns of BCI data as elements on the manifold of positive semi-definite (PSD) matrices. Under this novel framework, BCI processing and calibration time will be significantly reduced, and the system will become more robust to small perturbations, with the potential to greatly benefit people suffering from severe motor impairments. This manifold-based framework can be broadly applied to other disciplines, including biology, agriculture, neuroscience, and computer vision. The research combines ideas from mathematics, statistics, and computational methods, thereby attracting students with diverse backgrounds and helping broaden the participation of underrepresented groups in STEM. The results will be integrated into both undergraduate and graduate Data Science courses; the mathematical foundations and computational implementation of this research will be disseminated through publications, conference presentations, and open-source code. The novel framework being used is that of the manifold of PSD matrices equipped with a new metric known as the Bures-Wasserstein (BW) metric. This formulation has the advantage that the computation of the distance induced by the BW metric is twice as fast as for the usual Riemannian distance, hence more efficient, while being robust to small perturbations. The following research themes will be explored. First the mathematical properties of the BW distance and its induced geometry on the manifold of PSD matrices will be studied. Three algorithms will be developed for computing the barycenter (under the BW distance) of a collection of PSD matrices. A class of Gaussian-like distributions will then be introduced on the manifold of PSD matrices, and a theory of statistical inference will be investigated through maximum likelihood estimates. To classify PSD matrices into the distinct groups associated with the different actions intended by the BCI user, Gaussian mixture models will be developed, and non-parametric approaches used with the help of kernel functions on the tangent space of the manifold. Finally, two methods for generating synthetic PSD matrices on the manifold will be developed to shorten the calibration of the BCI.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项的全部或部分资金来源于《2021 年美国救援计划法案》（公法 117-2）。脑机接口 (BCI) 是一种基于计算机的系统，可在人脑和外部设备之间建立通信路径。 BCI 获取大脑信号并将其转换为外部设备的命令，以执行用户想要的操作。脑机接口在帮助患有严重运动障碍的人、检测和诊断健康问题以及为游戏等应用提供新界面方面表现出了巨大的潜力。已经使用了多种方法来处理 BCI 数据，这些数据本质上主要是空间和时间数据，例如多通道脑电图和功能磁共振成像。不幸的是，由于对伪影、噪声和异常值的敏感性，现有技术仍然存在鲁棒性和可靠性低的问题，并且需要长时间的校准。这些挑战将通过开发一种新颖的框架来解决，该框架可以有效、稳健地对与 BCI 数据的空间和时间模式相关的协方差矩阵进行建模，作为正半定 (PSD) 矩阵流形上的元素。在这个新颖的框架下，BCI 处理和校准时间将显着减少，系统对小扰动将变得更加鲁棒，有可能使患有严重运动障碍的人们受益匪浅。这种基于流形的框架可以广泛应用于其他学科，包括生物学、农业、神经科学和计算机视觉。该研究结合了数学、统计学和计算方法的思想，从而吸引了不同背景的学生，并帮助扩大 STEM 中代表性不足的群体的参与。研究结果将被纳入本科生和研究生数据科学课程中；这项研究的数学基础和计算实施将通过出版物、会议演讲和开源代码进行传播。所使用的新颖框架是配备有称为 Bures-Wasserstein (BW) 度量的新度量的 PSD 矩阵流形的框架。该公式的优点是 BW 度量引起的距离的计算速度是通常黎曼距离的两倍，因此更高效，同时对小扰动具有鲁棒性。将探讨以下研究主题。首先将研究 BW 距离的数学性质及其在 PSD 矩阵流形上的导出几何形状。将开发三种算法来计算 PSD 矩阵集合的重心（在 BW 距离下）。然后将在 PSD 矩阵流形上引入一类类高斯分布，并通过最大似然估计来研究统计推断理论。为了将 PSD 矩阵分类为与 BCI 用户预期的不同操作相关的不同组，将开发高斯混合模型，并在流形切线空间上的核函数的帮助下使用非参数方法。最后，将开发两种在流形上生成合成 PSD 矩阵的方法，以缩短 BCI 的校准时间。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Topological Data Analysis for Scalp EEG Signal Processing

头皮脑电信号处理的拓扑数据分析

• DOI: 10.1109/icsip57908.2023.10270899
• 发表时间: 2023-07-08
• 期刊: 2023 8th International Conference on Signal and Image Processing (ICSIP)
• 作者: Jingyi Zheng;Ziqin Feng;Yuexin Li;Fan Liang;Xuan Cao;Linqiang Ge
• 通讯作者: Linqiang Ge