Collaborative Research: Accurate, Efficient and Robust Computational Algorithms for Detecting Changes in a Scene Given Indirect Data

从收集的数据的时间序列中检测变化在各种应用中非常重要，包括语音识别、医疗监控、信用卡欺诈检测、自动目标识别和视频监控。在医疗监测等应用中，找到发生变化的位置是非常重要的。在诸如视频监视的其他应用中，改变的类型，例如感兴趣对象的移动或插入/删除，也是关键的。虽然从直接数据(例如，已经形成的图像)中检测这种变化已经被很好地研究，但在许多应用中，例如磁共振成像(MRI)、超声波和合成孔径雷达(SAR)，间接地获取数据的时间序列。检测这些应用中的变化的典型方法是首先形成感兴趣的图像或信号。结果，存储在间接数据中的可能对检测变化有价值的信息经常丢失。因此，该项目寻求开发准确、高效和健壮的计算算法，用于从给定的间接数据的时间序列中检测信号或图像的变化，而无需首先重建感兴趣的信号或图像。此外，该项目寻求纳入变化信息，以开发更好的图像和信号重建算法。研究生和本科生都将参与研究调查，以加强他们在科学和工程领域的职业准备。参与者将在公开可用的数据集上应用这些新技术，特别是在核磁共振、超声波和合成孔径雷达应用中获得的数据集。PI将使用框架理论、优化和统计方面的工具来开发和严格分析新的变化检测和图像/信号恢复算法。具体地说，PIS将解决拟议工作中的以下技术问题：(1)将先验信息与适当的数学/统计公式结合在模型中；(2)从间接数据序列中提取对象的旋转/平移；(3)通过统计分析调整模型参数；(4)在恢复算法中使用信号内和信号间的相关性；(5)为所产生的大型优化模型设计分布式算法。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Detecting change from a temporal sequence of collected data is important in a wide variety of applications, including speech recognition, medical monitoring, credit card fraud detection, automated target recognition, and video surveillance. In applications such as medical monitoring, it is very important to find where the change occurs. In other applications, such as video surveillance, the type of change, e.g. the movement or insertion/deletion of an object of interest, is also critical. While detecting such changes from direct data (e.g. images already formed) has been well studied, there are many applications, such as magnetic resonance imaging (MRI), ultrasound, and synthetic aperture radar (SAR) where the temporal sequence of data are acquired indirectly. The typical approach to detecting changes in these applications would be to first form the image or signal of interest. As a consequence, information that is stored in the indirect data that may be valuable to detecting change is often lost. Therefore, this project seeks to develop accurate, efficient, and robust computational algorithms for detecting changes in a signal or image from a given temporal sequence of indirect data without first reconstructing the signal or image of interest. Additionally, the project seeks to incorporate the change information to develop better image and signal reconstruction algorithms. Both graduate and undergraduate students will be involved in the research investigations to enhance their career preparation in science and engineering. The participants will apply these new techniques on publicly available data sets, notably obtained for MRI, ultrasound, and SAR applications. The PIs will employ tools in frame theory, optimization, and statistics to develop and rigorously analyze new change detection and image/signal recovery algorithms. Specifically, the PIs will address the following technical issues in the proposed work: (1) the incorporation of prior information with appropriate mathematical/statistical formulation in the model; (2) the extraction of rotation/translation of an object from a sequence of indirect data; (3) model parameters tuning through statistical analysis; (4) the employment of intra- and inter-signal correlations in the recovery algorithms; (5) the design of distributed algorithms for the resulting large-size optimization model.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.