Optimal compressive sensing systems for signal acquisition, reconstruction and processing

用于信号采集、重建和处理的最佳压缩传感系统

• 批准号: 4062-2011
• 负责人: Lu, WuSheng
• 金额: $ 2.33万
• 依托单位: University of Victoria
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=509626
• 关键词: Optimal; compressive; sensing; systems; signal

In a nutshell, a compressive sensing (CS) system acquires a signal of interest indirectly by correcting a small number of its "projections" rather than evenly sampling it at the so-called Nyquist rate which can be prohibitively high for broadband signals encountered in many applications. This new signal acquisition paradigm has revolutionized the way digital data are traditionally acquired. The objectives of the proposed research are threefold. First, we aim at developing optimal CS systems that require fewer-than-ever number of measurements that yet contain complete information of the data. This entails reduced number of sensing devices (or lower software complexity in the case of software implementation), hence improving processing efficiency and reducing cost. This goal will be achieved by exploring and maximizing a new measure for the incoherence between the measurement subsystem and an overcomplete dictionary for sparse representation of signals. Second, we investigate new methods to recover the data of interest from the limited number of measurements with better accuracy relative to existing algorithms. Our interest is in large-scale data, hence we must develop fast algorithms for them to be useful in real-time data processing. To this end, we shall develop a class of proximal-gradient algorithms for solving Lp type (with p < 1) mixed convex-nonconvex problems. Third, the algorithms developed are to be applied to problems in digital signal processing such as de- nosing, de-blurring and segmentation in medical imaging and communications such as wireless channel estimation and message recovery problems. These problems are current, significant and technically challenging in their respective fields either because of their involvement in large amount of data (medical imaging) or because of their real-time nature (wireless communication applications). The information processing communities will regard our research endeavors as significant when the proposed algorithms begin to play a crucial role in solving these and other related problems with satisfactory processing speed and performance.

简而言之，压缩感测（CS）系统通过校正其少量的“投影”而不是以所谓的奈奎斯特速率对其进行均匀采样来间接地获取感兴趣的信号，奈奎斯特速率对于许多应用中遇到的宽带信号可能高得令人望而却步。这种新的信号采集模式彻底改变了传统的数字数据采集方式。拟议研究的目标有三个方面。首先，我们的目标是开发最佳的CS系统，需要比以往任何时候都少的测量，但包含完整的数据信息。这需要减少传感设备的数量（或者在软件实现的情况下降低软件复杂性），从而提高处理效率并降低成本。这一目标将通过探索和最大化测量子系统和信号稀疏表示的过完备字典之间的不相干性的新措施来实现。其次，我们研究了新的方法来恢复感兴趣的数据，从有限数量的测量更好的精度相对于现有的算法。我们的兴趣是在大规模的数据，因此，我们必须开发快速算法，他们是有用的实时数据处理。为此，我们将发展一类解Lp型（p < 1）混合凸-非凸问题的近似梯度算法。第三，所开发的算法将被应用于数字信号处理中的问题，例如医学成像和通信中的去噪、去模糊和分割，例如无线信道估计和消息恢复问题。这些问题在其各自的领域中是当前的、重要的和技术上具有挑战性的，这是因为它们涉及大量数据（医学成像）或因为它们的实时性质（无线通信应用）。当我们提出的算法开始以令人满意的处理速度和性能在解决这些和其他相关问题中发挥关键作用时，信息处理界将把我们的研究努力视为重要的。