摘要翻译：
实时有效地匹配大脑对重复性视觉刺激反应频率的能力是可靠的基于SSVEP的脑机接口(BCI)的基础。将不同刺激的检测作为一个复合假设检验，假设SSVEP在Ramanujan周期变换(RPT)字典中具有稀疏表示。对于二进制情况，我们基于广义似然比检验建立并分析了RPT检测器的性能。我们的方法被扩展到多假设多电极设置，在那里我们用预刺激数据捕获电极之间的空间相关性。我们还提出了一种新的评估SSVEP检测方案的指标，该指标基于在给定系统资源下SSVEP检测方案的可实现效率和识别率的折衷。利用汇流超几何函数，得到了检验统计量的精确分布。基于合成数据和真实数据的大量模拟结果表明，RPT探测器的性能明显优于基于光谱的方法。它的性能也超越了最先进的典型相关分析(CCA)方法，在精度和样本复杂度方面，短数据长度的制度是关键的实时应用。该方法是渐近最优的，因为它随着数据长度的增加而将间隙关闭到一个完美的测量界。与现有的高度依赖数据的监督方法相比，RPT检测器仅使用预刺激数据来估计每个被试的空间相关性，从而省去了大量被试和刺激数据收集的大量开销。我们的工作推进了新兴的实时脑机接口的理论和实践，并提供了一个新的框架来比较SSVEP检测方案在更广的工作范围内。
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英文标题：
《Detection of Brain Stimuli Using Ramanujan Periodicity Transforms》
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作者：
Pouria Saidi, Azadeh Vosoughi and George Atia
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  The ability to efficiently match the frequency of the brain's response to repetitive visual stimuli in real time is the basis for reliable SSVEP-based Brain-Computer-Interfacing (BCI). The detection of different stimuli is posed as a composite hypothesis test, where SSVEPs are assumed to admit a sparse representation in a Ramanujan Periodicity Transform (RPT) dictionary. For the binary case, we develop and analyze the performance of an RPT detector based on a derived generalized likelihood ratio test. Our approach is extended to multi-hypothesis multi-electrode settings, where we capture the spatial correlation between the electrodes using pre-stimulus data. We also introduce a new metric for evaluating SSVEP detection schemes based on their achievable efficiency and discrimination rate tradeoff for given system resources. We obtain exact distributions of the test statistic in terms of confluent hypergeometric functions. Results based on extensive simulations with both synthesized and real data indicate that the RPT detector substantially outperforms spectral-based methods. Its performance also surpasses the state-of-the-art Canonical Correlation Analysis (CCA) methods with respect to accuracy and sample complexity in short data lengths regimes crucial for real-time applications. The proposed approach is asymptotically optimal as it closes the gap to a perfect measurement bound as the data length increases. In contrast to existing supervised methods which are highly data-dependent, the RPT detector only uses pre-stimulus data to estimate the per-subject spatial correlation, thereby dispensing with considerable overhead associated with data collection for a large number of subjects and stimuli. Our work advances the theory and practice of emerging real-time BCI and affords a new framework for comparing SSVEP detection schemes across a wider spectrum of operating regimes.
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PDF链接：
https://arxiv.org/pdf/1801.09161