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检测变化在各种各样的应用中是重要的，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，找到变化发生的位置非常重要。在其他应用中，例如视频监控，变化的类型，例如感兴趣对象的移动或插入/删除，也是至关重要的。 虽然已经很好地研究了从直接数据（例如，已经形成的图像）检测这种变化，但是存在许多应用，例如磁共振成像（MRI）、超声和合成孔径雷达（SAR），其中间接地采集数据的时间序列。在这些应用中检测变化的典型方法是首先形成感兴趣的图像或信号。 因此，存储在间接数据中的对检测变化可能有价值的信息常常丢失。因此，该项目旨在开发准确，高效和鲁棒的计算算法，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，该项目还寻求将变化信息结合起来，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，以提高他们在科学和工程方面的职业准备。 参与者将把这些新技术应用于公开的数据集，特别是MRI、超声和SAR应用。 PI将使用框架理论，优化和统计学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。具体而言，研究员将在拟议的工作中解决以下技术问题：（1）将先验信息与适当的数学/统计公式结合在模型中;（2）从一系列间接数据中提取物体的旋转/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）在恢复算法中使用信号内和信号间的相关性。（5）为最终的大规模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知识价值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.