项目标书摘要：在使用像是匹配逼近(matching pursuits,MP)或是正交匹配逼近(orthogonal matching pursuits,OMP)之类的贪婪演算法以求得到讯号的稀疏表示法时，经常收敛到区域最小值。举例来说，当EEG 及ECG 讯号被非高斯杂讯所干扰时，在计算其稀疏表示式时，就经常出现这种缺点。本计划将延伸及改进 Durka 提出的随机搜寻法，能够在适当的复杂度下，求出非高斯讯号的稀疏表示法。我们的研究也计画发展下列三种技巧及并整合在随机搜寻的演算法中：利用以Fisher资讯量为基础的自然Riemannian梯度用来处理搜寻空间的非欧几何特性；使用Grassmannian frames of quadratic Gabor chirplets 当作过完备的讯号原子库(dictionary),对於经过时移/频移或缩放之後的讯号，这个原子库具有最大的异调性(maximally incoherence);使用随机弥集演算法(probabilistic memetic algorithms)以平衡随机全域搜寻(使用Grassmannian Gabor frames)及最陡下降区域搜寻(利用自然梯度)之间的计算负荷。将自然梯度、传统Gabor 原子的Grassmannian frame 及Gabor chirplets 的Grassmannian frames 逐步加入弥集演算法之後，将得出三种不同的搜寻演算法。这些演算法将用来解得多通道EEG 及其ICA 成份的稀疏表示法。和MP 演算法及OMP 演算法的效能作一比较後，可以验证我们演算法的有效性与效率。除了将理论及各项分析结果发表於期刊或国际会议，本计划亦将公开演算法的MATLAB 程式。交通大学脑科学研究中心的国际合作学者锺子平教授(Prof.Tzyy-Ping Jung),目前任教於Institute for Neural Computation at the Swartz Institute in University of California at San-Diego(UCSD),已经同意担任本计划的谘询顾问。
Application Abstract: Greedy algorithms for obtaining sparse representations——such as matching pursuits(MP)and orthogonal matching pursuits(OMP)——are often trapped in local minima when the target signals are quasi-sparse in nature.This handicap manifests itself most profoundly in real world applications for example the sparse representations of EEG and ECG signals when the target signals are contaminated by non-Gaussian“artifacts”.In this project,we intend to expand and improve the stochastic search strategies proposed by Durka with the specific goal of finding the sparest approximations of quasi-sparse non-Gaussian signals at modest computation costs.Our research will focus on the development and integration of three novel techniques into stochastic search algorithms:■ Natural Riemannian Gradients based on Fisher information will be used to account for the non-Euclidean geometry of the search space;■ Grassmannian Frames of Quadratic Gabor Chirplets that exhibit maximally incoherence among elements undergone time-frequency translations,scaling and sheering will serve as the over-complete dictionaries;■ Probabilistic Memetic Algorithms will be employed to balance the computation workload of randomized global searches(based on Grassmannian Gabor frames)and steepest-descend local searches(using natural gradients).We will produce three different versions of search algorithm by adding natural gradient adaptation,Grassmannian frames of classical Gabor atoms and Grassmannian frames of Gabor chirplets incrementally to the memetic algorithms.These algorithms will be employed to obtain the sparest representations of multi-channel recordings of EEG sensory-motor event related potentials(ERPs)and their ICA components.We shall test the effectiveness and efficiency of these algorithms by comparing their performance against those of MP and OMP algorithms.Both theoretical contributions and analytical results will be published.MATLAB implementation of these algorithms will also be made available to the public.Long-term collaborator of NCTU Brain Research Center,Prof.Tzyy-Ping Jung(锺子平)of the Institute for Neural Computation at the Swartz Institute in University of California at San-Diego(UCSD),has agreed to serve as an advisory consultant to this project.
