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

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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.