Compressive sensing using iterative hard thresholding with low precision data representation: Theory and applications

N.M. Gurel, K. Kara, A. Stojanov, T. Smith, T. Lemmin, D.-A. Alistarh, M. Puschel, C. Zhang, IEEE Transactions on Signal Processing (2020).


Journal Article | Epub ahead of print | English

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Author
Gurel, Nezihe Merve; Kara, Kaan; Stojanov, Alen; Smith, Tyler; Lemmin, Thomas; Alistarh, Dan-AdrianIST Austria; Puschel, Markus; Zhang, Ce
Department
Abstract
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 speedup with negligible loss of recovery quality.
Publishing Year
Date Published
2020-07-20
Journal Title
IEEE Transactions on Signal Processing
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eISSN
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Gurel NM, Kara K, Stojanov A, et al. Compressive sensing using iterative hard thresholding with low precision data representation: Theory and applications. IEEE Transactions on Signal Processing. 2020. doi:10.1109/TSP.2020.3010355
Gurel, N. M., Kara, K., Stojanov, A., Smith, T., Lemmin, T., Alistarh, D.-A., … Zhang, C. (2020). Compressive sensing using iterative hard thresholding with low precision data representation: Theory and applications. IEEE Transactions on Signal Processing. https://doi.org/10.1109/TSP.2020.3010355
Gurel, Nezihe Merve, Kaan Kara, Alen Stojanov, Tyler Smith, Thomas Lemmin, Dan-Adrian Alistarh, Markus Puschel, and Ce Zhang. “Compressive Sensing Using Iterative Hard Thresholding with Low Precision Data Representation: Theory and Applications.” IEEE Transactions on Signal Processing, 2020. https://doi.org/10.1109/TSP.2020.3010355.
N. M. Gurel et al., “Compressive sensing using iterative hard thresholding with low precision data representation: Theory and applications,” IEEE Transactions on Signal Processing, 2020.
Gurel NM, Kara K, Stojanov A, Smith T, Lemmin T, Alistarh D-A, Puschel M, Zhang C. 2020. Compressive sensing using iterative hard thresholding with low precision data representation: Theory and applications. IEEE Transactions on Signal Processing.
Gurel, Nezihe Merve, et al. “Compressive Sensing Using Iterative Hard Thresholding with Low Precision Data Representation: Theory and Applications.” IEEE Transactions on Signal Processing, IEEE, 2020, doi:10.1109/TSP.2020.3010355.
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