CAREER: Optimizations for Sparse Solutions and Applications

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In many areas such as signal processing, control, statistics, learning, inverse problems, and management, "large" data sets are often processed to find "small" solutions, those depending ultimately upon a small number of factors. Since these solutions tend to be sparse in a way, it is possible for methods that pick out the sparse solutions to find them from a reduced number of indirect measurements compared to what are usually considered necessary. This is the emerging technology of compressed sensing (CS). In this research, the PI proposes to study a broad range of issues and techniques to advance CS. His proposed reseach includes the introduction of new methodolgies for exploiting solution sparsity to accelerate CS computation, the development of algorithms that utilize operations requiring low storage and maintain robustness to noise and errors in data, and the discovery of efficient methods for minimizing the l1-norms of wide classes of functions such as first and higher-order differences. This project will include an integrated educational program involving a new course, one Ph.D. student, and the participation in the Rice-Houston AGEP program in producing competitive women and minority graduate students.The new emerging technology of "compressed sensing" is a complement to traditional data compression. While the traditional technology encodes digital data using fewer bits in order to save storage and transmission time, the new technology can significantly reduce the time, energy, and cost associated with the acquisition of digital data. This is achieved by acquiring digit information of an object of interest from a reduced number of obervations than what is usually necessary. For example, the life of an aeriel such as a space telescope can be greatly extended due to a lower sampling rate (and thus a lower power demand). Hyperspectral and infrared imaging devices can produce the same images with smaller sensors, or if with the same sensors, images at higher resolution. As such, the new technology can lead to breakthroughs for applications where the bottleneck lies in the high cost of data acquisition.