Practical Optimization Algorithms for Large-Scale Image and Data Processing

优化算法是解决图像和数据处理中许多问题的核心，而专用算法在实际应用中往往至关重要。首席研究员（PI）将在两个重要领域进行算法研究：图像反卷积和压缩感知，以开发使相关方法适用于大规模实际应用的算法。对于图像反卷积，PI旨在为基于总变化的模型开发优化算法，该算法比现有算法至少快一个或多个数量级。初步研究表明，这一雄心勃勃的目标完全可以实现。新的压缩感知（CS）方法可以显著减少重建可压缩数据所需的测量次数。PI建议为CS的重要现实应用开发算法，并研究随机克罗内克积测量矩阵，这可以大大降低数据重建的复杂性。MRI（磁共振成像）是一种广泛使用的医学成像方式，从扫描数据创建图像。一次典型的腹部扫描大约需要90分钟。最近，一种名为压缩感知（CS）的新方法取得了进展，可以通过只扫描三分之一的数据，将这段时间缩短到30分钟，同时保持良好的图像质量。然而，这种可能性只有在快速算法可以对不完整数据进行实时处理的情况下才能实现。这个项目就是开发和分析这样的快速算法。另一类要研究的快速算法是用于提高模糊图像的清晰度。例如，有了这样快速的算法，卫星图像或医学图像就可以更好、更及时地进行分析。该项目的成果将影响从信息技术到生物技术的各种应用。

Optimization algorithms are at the core of solving many problems in image and data processing, and dedicated algorithms are often critical in real-world applications. The principal investigator (PI) will conduct algorithmic research in two important areas: image deconvolution and compressive sensing, to develop enabling algorithms that make relevant methodologies practical for large-scale, real applications. For image deconvolution, the PI aims to develop optimization algorithms for total-variation-based models that are faster than existing algorithms by at least one or more order of magnitude. Preliminary studies have shown that this ambitious goal is well within grasp. The new compressive sensing(CS) methodologies make it possible to significantly reduce the number of measurements needed for reconstructing compressible data. The PI proposes to develop algorithms for important real-world applications of CS, and study random Kronecker-product measurement matrices that can drastically reduce data reconstruction complexity.MRI (magnetic resonance imaging) is a widely used medical imaging modality that creates an image from scanned data. A typical abdominal scan may take around 90 minutes. Recent progress in a new methodology called compressive sensing (CS) makes it possible to reduce this time to 30 minutes by scanning only one third of data, while maintaining good image quality. However, such a possibility can be realized only when fast algorithms are available to do real-time processing on incomplete data. This project is to develop and analyze such fast algorithms. Another class of fast algorithms to be investigated is for improving the clarity of fuzzy images. With such fast algorithms, for example, satellite or medical images can be better analyzed in a more timely fashion. The results of this project will impact applications ranging from information technology to biotechnology.