Multiscale Signal Processing for Next Generation Electroencephalography

这一建议寻求开发一个全新的多尺度框架，用于多变量现实世界过程的数据自适应探索性分析。这将通过严格处理通道内和通道间的固有信号特征、跨越时间、空间、频率和熵来实现。特别强调没有统计假设和数学假象的方法，并与多变量数据中固有的时变振荡模式相匹配。这将有助于绕过与当前使用的技术(傅立叶、小波)相关的数学障碍，这些技术依赖于固定的基函数和积分变换，从而使表示变得有色，限制了它们的精度，并限制了它们在涉及真实世界漂移和噪声信息的问题中的适用性。对于多尺度数据，当前的统计和信息理论方法是不够的，因为它们将表明共享共同噪声但不包含相同有用信号的两个数据通道的高度相关性。拟议的数据自适应分析框架将解决这些问题，并将创建自然的“内在”数据关联措施(内在多重关联、内在多重信息)。虽然当前的单变量数据自适应方法具有巨大的潜力，但它们不适合直接应用于多变量或异构源，因为它们必然会为每个数据通道创建不同数量的基函数。可穿戴系统，如身体传感器网络，努力在性能和用户利益(低成本、易用性)之间找到平衡，并需要下一代信号处理工具来确定它们能够产生有价值信息的程度。该提案的主旨是开发严谨、数据自适应、紧凑和物理上有意义的信号处理解决方案，以便为多传感器和可穿戴技术的进步提供算法支持。我们自己的最初的多变量数据自适应解决方案显示出巨大的前景；它们需要进一步开发和全面测试，以显示旋转相关(非圆形)分布、功率不平衡、不确定性和噪声的数据。借助于算法设计中的非线性优化以及动态复杂性科学和多分辨率信息论的见解，我们的方法有望在多变量数据分析方面向前迈出一大步，并产生重大的长期影响。该方案的成功结果将为依赖于多传感器数据的领域的发展开辟新的可能性，并为处理多通道记录中的不确定性、非圆形、复杂性和非平稳性的应用开辟新的前沿。为了最大化这项工作的短期到中期影响和成本效益，我们与伦敦的皇家布朗普顿睡眠诊所和丹麦的奥胡斯大学合作，考虑将新兴的可穿戴技术应用于大脑监测。

This proposal seeks to develop a fundamentally new multiscale framework for data-adaptive exploratory analysis of multivariate real-world processes. This will be achieved through a rigorous treatment of both within- and cross-channel intrinsic signal features, spanning time, space, frequency and entropy. Particular emphasis will be on approaches that are free of statistical assumptions and mathematical artefacts, and match the time-varying oscillatory modes inherent in multivariate data. This will help bypass the mathematical obstacles associated with currently used techniques (Fourier, wavelet), which rely on fixed basis functions and integral transforms, thus colouring the representation, limiting their accuracy, and restricting their applicability in problems involving real-world drifting and noisy information.For multiscale data current statistical and information theoretic measures are inadequate, as they will indicate high correlation for two data channels that share common noises, but do not contain the same useful signal. The proposed data-adaptive analysis framework will resolve such issues, and will create natural "intrinsic" data association measures (intrinsic multi-correlation, intrinsic multi-information). While current univariate data-adaptive approaches have enormous potential, they are not suitable for direct application to multivariate or heterogeneous sources, as they are bound to create a different number of basis functions for every data channel.Wearable systems, such as bodysensor networks, strive to find a balance between performance and user benefits (low cost, ease of use), and require next-generation signal processing tools to establish the extent to which they can produce valuable information. The thrust of this proposal is on developing rigorous, data-adaptive, compact, and physically meaningful signal processing solutions in order to provide an algorithmic support for progress in multi-sensor and wearable technologies. Our own initial multivariate data-adaptive solutions show great promise; they need to be further developed and comprehensively tested for data exhibiting rotation-dependent (noncircular) distributions, power imbalance, uncertainty, and noise. With the aid of nonlinear optimisation in the algorithmic design and insights from dynamical complexity science and multiresolution information theory, our approach promises a quantum step forward in multivariate data analysis, and a significant long-term impact.The successful outcomes of this proposal will open radically new possibilities for advances in areas that depend on multi-sensor data, and a new front of research in applications dealing with uncertainty, noncircularity, complexity, and nonstationarity in multi-channel recordings. To maximise the short- to medium-term impact of this work and for cost effectiveness, we consider applications in emerging wearable technologies for brain monitoring, in collaboration with the Royal Brompton Sleep Clinic in London and Aarhus University in Denmark.