Accurate digital representation and recovery for redundant frames

冗余帧的准确数字表示和恢复

• 批准号: 0811086
• 负责人: Alexander Powell
• 金额: $ 12.31万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0811086&HistoricalAwards=false
• 关键词: Accurate; digital; representation; recovery; redundant

Redundant frame representations play a central role in signal processing applications. By using overcomplete systems to represent signals, frames offer increased design flexibility and are thereby able to provide robustness against noise and data loss in many settings. The investigator studies the mathematics of digitally representing redundant finite frame expansions, with an emphasis on two key steps: coefficient quantization and signal reconstruction. The work on quantization (the encoding step) focuses on the class of Sigma-Delta algorithms and studies rigorous approximation error bounds, dual frame methods for boosting performance, and the design of new algorithms for multiple description coding and orthogonal frequency division multiplexing. Sigma-Delta algorithms are well suited for utilizing the correlations inherent in redundant collections of frame coefficients, and are desirable in practice since they can be robustly implemented using very coarse, for example one bit, scalar quantizers. In the work on signal recovery (the decoding step), the investigator studies new nonlinear consistent reconstruction algorithms for analog-to-digital conversion in the settings of Pulse Code Modulation and Sigma-Delta quantization. The investigator also studies how to extend noise-shaping and consistent reconstruction methods to distributed processing applications based on fusion frames.Digital data is ubiquitous in modern technology. The project addresses the general problem of how to accurately process, transmit, and recover digital signals in noisy environments. The massive size of many digital data sets drives a need for new mathematical techniques that are capable of providing efficient and robust data processing algorithms. The work on quantization of fusion frames applies to scenarios where a dense collection of low resolution sensors is deployed in a remote environment; the project studies methods for optimally communicating and extracting digital information through the sensor network. The work on quantization of finite frame expansions is applicable to communication over erasure channels where physical constraints or other interference result in a loss of transmitted information; the project studies procedures for mitigating the effect of data erasures.

冗余框架表示在信号处理应用中起着核心作用。 通过使用过度的系统来表示信号，框架提供了提高的设计灵活性，从而可以在许多设置中提供稳健性，以防止噪声和数据丢失。 研究人员研究了代表冗余框架扩展的数字数学，重点是两个关键步骤：系数量化和信号重建。 量化（编码步骤）的工作着重于Sigma-Delta算法的类别和研究严格的近似误差界限，提高性能的双帧方法以及用于多重描述编码和正交频次频施加的新算法的设计。 Sigma-Delta算法非常适合利用帧系数冗余集合中固有的相关性，并且在实践中是可取的，因为它们可以使用非常粗糙的（例如一个位，标量量化器）来牢固地实现。 在信号恢复的工作（解码步骤）中，研究人员在脉冲代码调制和Sigma-Delta量化的设置中研究了新的非线性一致重建算法，以用于类似于数字的转换。 研究人员还研究了如何将噪声形成和一致的重建方法扩展到基于融合框架的分布处理应用程序。数字数据在现代技术中无处不在。 该项目解决了如何在嘈杂环境中准确处理，传输和恢复数字信号的一般问题。 许多数字数据集的庞大规模驱动了能够提供有效且强大的数据处理算法的新数学技术的需求。 量化融合框架的工作适用于将密集的低分辨率传感器集合部署在远程环境中的方案；项目研究方法是通过传感器网络最佳通信和提取数字信息的方法。 有限帧扩展的量化工作适用于在物理约束或其他干扰导致传输信息丢失的擦除通道上的通信；减轻数据擦除作用的项目研究程序。