Compressive Sensing Using Iterative Hard Thresholding with Low Precision Data Representation: Theory and Applications

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 r...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 68; p. 1
Main Authors: Gurel, Nezihe Merve, Kara, Kaan, Stojanov, Alen, Smith, Tyler, Lemmin, Thomas, Alistarh, Dan, Puschel, Markus, Zhang, Ce
Format: Journal Article
Language:English
Published: New York IEEE 01.01.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Compressed sensing
Compression ratio
Compressive sensing
Data compression
Extraterrestrial measurements
Instruments
Iterative methods
Magnetic resonance imaging
Mathematical analysis
Matrix algebra
Matrix methods
Medical imaging
Noise measurement
normalized IHT
Optimization
Quantization (signal)
Radio astronomy
Representations
stochastic quantization
Thresholding (Imaging)
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2020.3010355