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.
