CAREER: Practical Compressive Signal Processing

Claremont Mckenna College, Claremont CA

Investigators

Abstract

A "signal" is any data set that one would like to acquire, for example, an image, a large block of data, or an audio clip. One can imagine asking how quickly one would need to sample an audio clip so that from those samples alone, the audio clip could be accurately recovered. Would you need to sample every nanosecond, every millisecond, or every second? Compressive Signal Processing (CSP) shows that the important information in many signals can be obtained and recovered from far fewer samples than traditionally thought. The applications of CSP are widespread and include imaging (medical, hyperspectral, microscopy, biological), analog-to-information conversion, radar, large scale information synthesis, geophysical data analysis, computational biology, and many more. Although these applications are astounding, there has been a disconnect between the theoretical work in CSP and the use of CSP in practical settings. The goals of this project will bridge this gap by providing methods and analysis for CSP that apply to real-world signals and settings. Such work will lead to decreased scan time in MRI, reduced cost and energy consumption in computing infrastructures, improved detection of diseased crops from hyperspectral images, increased accuracy in radar, and improved compression and analysis in many other large-data applications. In addition, this project will involve students at all levels and introduce them to rigorous scientific research. The PI actively recruits members from under-represented populations, and will continue to promote diversity through her own research and outreach programs. Early CSP models restrict the class of signals to those compressible in a very specific sense (sparse with respect to an orthonormal or incoherent basis). One goal of this project is to relax this restriction to allow for signals actually encountered in practice, such as those sparse in redundant, coherent, and highly overcomplete dictionaries. We will utilize both greedy approaches and optimization-based methods, tailored to specific dictionaries of interest, as well as more general methods for arbitrary bases. In addition, this project will develop adaptive CSP sampling schemes, where measurements of the signal are designed "on the fly," as they are being taken. Traditional measurement schemes ignore this information, while adaptive schemes have the potential to significantly reduce reconstruction error, number of measurements, and computation time. We will identify optimal measurement strategies for constrained and unconstrained settings, and analyze how much one can actually gain from adaptivity from an information theoretic point of view. The project will also involve work in "one-bit CSP", a new and exciting branch of CSP which handles extreme (and often more realistic) quantization. We will draw on sub-linear methods, where large errors appear naturally, and also use optimization based techniques along with adaptive quantization thresholds to reduce the recovery error below the best possible for non-adaptive quantization. In studying these topics, the research will bridge a large gap in the theory of CSP and provide a unified framework for both practitioners and researchers.