Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 68, Issue -, Pages 4268-4282Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2020.3010355
Keywords
Compressed sensing; Extraterrestrial measurements; Noise measurement; Quantization (signal); Thresholding (Imaging); Instruments; Magnetic resonance imaging; Compressive sensing; normalized IHT; data compression; stochastic quantization
Categories
Funding
- Swiss Data Science Center
- Alibaba
- Google Focused Research Awards
- Huawei
- MeteoSwiss
- Oracle Labs
- Swisscom
- Zurich Insurance
- Chinese Scholarship Council
- Department of Computer Science at ETH Zurich
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Modern scientific instruments produce vast amounts of data, which can overwhelm the processing ability of computer systems. Lossy compression of data is an intriguing solution, but comes with its own drawbacks, such as potential signal loss, and the need for careful optimization of the compression ratio. In this work, we focus on a setting where this problem is especially acute: compressive sensing frameworks for interferometry and medical imaging. We ask the following question: can the precision of the data representation be lowered for all inputs, with recovery guarantees and practical performance? Our first contribution is a theoretical analysis of the normalized Iterative Hard Thresholding (IHT) algorithm when all input data, meaning both the measurement matrix and the observation vector are quantized aggressively. We present a variant of low precision normalized IHT that, under mild conditions, can still provide recovery guarantees. The second contribution is the application of our quantization framework to radio astronomy and magnetic resonance imaging. We show that lowering the precision of the data can significantly accelerate image recovery. We evaluate our approach on telescope data and samples of brain images using CPU and FPGA implementations achieving up to a 9x speed-up with negligible loss of recovery quality.
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