Applications of frames to speech recognition, distributed processing, bio-medical engineering and more

CasazzaDMS-0704216 研究人员和他的同事们致力于设计希尔伯特空间框架的应用。这包括直接与需要这种框架的团体合作，如西门子公司研究中心、卡内基梅隆大学生物医学工程中心和莱斯大学电气工程系的数字信号处理中心。其中一个项目涉及设计框架和算法，用于进行无相位信号重建。该项目旨在消除信号中的某些背景噪声，使语音信号更清晰。另一个项目涉及回答这样一个问题：成像在系统生物学中的作用是什么？ 其目标是建立一个分布式但集成的大型生物图像数据库，使研究人员能够上传数据、处理数据、共享数据、下载数据以及拥有平台优化的代码，所有这些都采用通用格式。第三个项目涉及做信号重建witherasures。 研究人员设计了一个系统，该系统不需要任何额外的系数计算，即快速又准确。 这种方法需要为存在传输丢失或擦除的无数应用程序定制设计。 另一个项目涉及为分布式处理中的问题设计“融合框架”。 这就需要设计一种局部框架，能够快速准确地全局融合数据，尤其是在数据丢失的情况下。这些被用于各种问题，包括传感器网络.另一个项目是寻找等范数等角Parseval框架和相互无偏基。这些框架在量子态层析成像、量子密码学和量子力学的基础问题中有着广泛的应用。 信号重建项目旨在清理某些类型的音频信号，这些信号中嵌入了噪声，以呈现更清晰的信号。 另一个项目涉及用来观察我们周围世界的传感器。 目前正在收集的传感数据的数量超过了在一个地方收集用于分析的数量。 研究人员和他的同事们正在设计智能的方法来减少被分析的原始数据量，这就需要理解测量中冗余的性质和作用。对我们对冗余信息的基本理解做出数学贡献，可以推进环境监测（包括农业技术）、军事监视、理解感觉神经系统的运作以及改进通用数据收集方法等问题的工程解决方案，这些方法可以有效地将自然界中的模拟事件转化为可供分析的数字信号。生物成像对准确的分类有着迫切的需求，其中一些涉及生死决策，目前对错误分类非常敏感（例如检测癌症时的假阴性决策）。 这里的目标是设计能够以接近完美的准确度进行分类的系统。

CasazzaDMS-0704216 The investigator and his colleagues work on designingHilbert space frames for applications. This involves workingdirectly with the groups needing such frames such as SiemensCorporate Research, the Bio-Medical Engineering Center atCarnegie Mellon University, and the Digital Signal ProcessingCenter in the Electrical Engineering department at RiceUniversity. One project involves designing frames and algorithmsfor doing signal reconstruction without phase. This project isdesigned to remove certain background noises from a signal sothat the voice signals are clearer. Another project involvesanswering the question: What is the role and what can imaging dofor systems biology? The goal is to have distributed yetintegrated large bioimage databases that would allow researchersto upload their data, have it processed, share the data, downloaddata as well as having platform-optimized code, all in a commonformat. A third project involves doing signal reconstruction witherasures. The investigator has designed a system that accountsfor erasures without any extra coefficient calculations, which isboth fast and accurate. This method needs to be custom designedfor the myriad of applications where there are transmissionlosses or erasures. Another project involves designing "fusionframes" for problems in distributed processing. This requiresdesigning localized frames that globally fuse data both quicklyand accurately -- especially in the face of losses. These areused for a variety of problems including sensor networks. Another project is geared to finding equal-norm equi-angularParseval frames and mutually unbiased bases. These frames areused in quantum state tomography, quantum cryptography andfoundational issues in quantum mechanics. The signal reconstruction project is designed to clean upcertain types of audio signals that have noise embedded in theirphase to present a clearer signal. Another project involvessensors that are used to observe the world around us. The amountof sensed data that is currently being collected is more than canbe collected in one place for analysis. The investigator and hiscolleagues are designing intelligent ways to reduce the amount ofraw data that is analyzed, and this necessitates understandingthe nature and role of the redundancy in the measurements. Making mathematical contributions to our fundamentalunderstanding of redundant information could advance theengineering solutions to problems in environmental monitoring(including agricultural technology), military surveillance,understanding the operation of sensory neural systems, andimproving general data collection methods that efficiently turnthe analog events in the natural world into digital signals readyfor analysis. Bioimaging has a serious need for accurateclassification, some of which involves life and death decisionsand are currently very sensitive to misclassification (such asfalse negative decisions in detecting cancer). The goal here isto design systems that are able to classify with close-to-perfectaccuracy.