Sparse Signal Acquisition via Compressed Sensing and Principal Component Analysis

Open access

Abstract

This paper presents a way of acquiring a sparse signal by taking only a limited number of samples; sampling and compression are performed in one step by the analog to information conversion. The signal is recovered with minimal information loss from the reduced data record via compressed sensing reconstruction. Several methods of analog to information conversion are described with focus on numerical complexity and implementation in existing embedded devices. Two novel analog to information conversion methods are proposed, distinctive by their computational simplicity - direct subsampling and subsampling with integration. Proposed sensing methods are intended for and evaluated with real water parameter signals measured by a wireless sensor network. Compressed sensing proves to reduce the data transfer rate by >80 % with very little signal processing performed at the sensing side and no appreciable distortion of the reconstructed signal.

[1] Donoho, D.L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52 (4), 1289-1306.

[2] Andráš, I., Dolinský, P., Michaeli, L., Šaliga, J. (2018). A time domain reconstruction method of randomly sampled frequency sparse signal. Measurement, 127, 68-77.

[3] Wu, L., Yu, K., Hu, Y., Wang, Z. (2014). CS-based framework for sparse signal transmission over lossy link. In IEEE International Conference on Mobile Ad Hoc and Sensor Systems, Philadelphia, USA. IEEE, 680-685.

[4] Liu, H., Xiao, D., Zhang, R., Zhang., Y., Bai, S. (2016). Robust and hierarchical watermarking of encrypted images based on Compressive Sensing. Signal Processing: Image Communication, 46, 41-51.

[5] Xiao, X., He, Q., Fu, Z., Xu, M., Zhang, X. (2016). Applying CS and WSN methods for improving efficiency of frozen and chilled aquatic products monitoring system in cold chain logistics. Food Control, 60, 656-666.

[6] Bellan, D., Pignari, S.A. (2015). Monitoring of electromagnetic environment along high-speed railway lines based on compressive sensing. Progress in Electromagnetics Research C, 58, 183-191.

[7] Craven, D., McGinley, B., Kilmartin, L., Glavin, M., Jones, E. (2016). Energy-efficient Compressed Sensing for ambulatory ECG monitoring. Computers in Biology and Medicine, 71, 1-13.

[8] Angayarkanni, V., Radha, S. (2016). Design of bandwidth efficient compressed sensing based prediction measurement encoder for video transmission in wireless sensor networks. Wireless Personal Communications, 87, 1-21.

[9] Talari, A., Rahnavard, N. (2016). CStorage: Decentralized compressive data storage in wireless sensor networks. Ad Hoc Networks, 37, 475-485.

[10] Zong, F., Eurydice, M.N., Galvosas, P. (2016). Fast reconstruction of highly undersampled MR images using one and two dimensional principal component analysis. Magnetic Resonance Imaging, 34, 227-238.

[11] Sun, Z., Wang, S., Chen, X. (2016). Feature-based digital modulation recognition using compressive sampling. Mobile Information Systems, 10, 9754162.

[12] Maceková, Ľ., Žiga, M. (2014). The wireless sensor network concept for measurement of water quality in water streams. Acta Electrotechnica et Informatica, 14 (2), 60-67.

[13] Šaliga, J., Žiga, M., Galajda, P., Drutarovský, M., Kocur, D., Maceková, Ľ. (2015). Wireless sensor network for river water quality monitoring. In XXI IMEKO World Congress “Measurement in Research and Industry”, Prague, Czech Republic. IMEKO, 1745-1750.

[14] Galajda, P., Drutarovský, M., Šaliga, J., Žiga, M., Maceková, Ľ., Marchevský, S., Kocur, D. (2015). Sensor node for the remote river quality monitoring. In MEASUREMENT 2015. Bratislava, Slovakia: IMS SAS, 313-316.

[15] Šaliga, J., Kocur, D., Galajda, P., Drutarovsky, M., Macekova, Ľ., Andráš, I., Michaeli, L. (2017). Multiparametric sensor network for water quality monitoring. In IMEKO TC19 Workshop on Metrology for the Sea, Naples, Italy. IMEKO, 123-126.

[16] Stojmenović, I. (2005). Energy scavenging and nontraditional power sources for wireless sensor networks. In Handbook of Sensor Networks: Algorithms and Architectures. John Wiley & Sons, 75-106.

[17] Daponte, P., De Vito, L., Rapuano, S., Tudosa, I. (2017). Analog-to-information converters in the wideband RF measurement for aerospace applications: Current situation and perspectives. IEEE Instrumentation & Measurement magazine, 20 (1), 20-28.

[18] Candes, E.J., Wakin, M.B. (2008). An introduction to compressive sampling. IEEE Signal Processing Magazine, 25 (2), 21-30.

[19] Fung, G., Mangasarian, O.L. (2011). Equivalence of minimal ℓ0 and ℓp-norm solutions of linear equalities, inequalities and linear programs for sufficiently small p. Journal of Optimization Theory and Applications, 151 (1), 1-10.

[20] Palese, L.L. (2018). A random version of principal component analysis in data clustering. Computational Biology and Chemistry, 73, 57-64.

[21] Phyniomark, A., Hu, H., Phukpattaranont, P., Limsakul, C. (2012). Application of linear discriminant analysis in dimensionality reduction for hand motion classification. Measurement Science Review, 12 (3), 82-89.

[22] Ji, Y., Sun, S., Xie, H.B. (2017). Stationary waveletbased two-directional two-dimensional principal component analysis for EMG signal classification. Measurement Science Review, 17 (3), 117-124.

[23] Oesterlein, T.G., Lenis, G., Luik, A., Verma, B., Schmitt, C., Dossel, O. (2014). Removing ventricular far field artifacts in intracardiac electrograms during stable atrial flutter using the periodic component analysis - proof of concept study. In Electrocardiology 2014: Proceedings of 41thInternational Congress on Electrocardiology. Bratislava, Slovakia: IMS SAS, 49-52.

[24] Rošťáková, Z., Rosipal, R. (2018). Time alignment as a necessary step in the analysis of sleep probabilistic curves. Measurement Science Review, 18 (1), 1-6.

[25] Huang, H., Ouyang, H., Gao, H., Guo, L., Li, D., Wen, J. (2016). A feature extraction method for vibration signal of bearing incipient degradation. Measurement Science Review, 16 (3), 149-159.

[26] Abari, O., Lim, F., Chen, F., Stojanović, V. (2013). Why analog-to-information converters suffer in highbandwidth sparse signal applications. IEEE Transactions on Cirsuits and Systems - I: Regular Papers, 60 (9), 2273-2284.

[27] Daponte, P., De Vito, L., Iadarola, G., Iovini, M., Rapuano, S. (2016). Experimental comparison of two mathematical models for Analog-to-Information Converters. In 21st IMEKO TC4 Symposium “Measurements of Electrical Quantities 2016” (and 19th International Workshop on ADC and DCA Modelling and Testing, IWADC): Understanding the World Through Electrical and Electronic Measurement, Budapest, Hungary. IMEKO, 65-70.

[28] Daponte, P., De Vito, L., Iadarola, G., Rapuano, S. (2016). PRBS non-idealities affecting Random Demodulation Analog-to-Information Converters. In 21stIMEKO TC4 Symposium “Measurements of Electrical Quantities 2016” (and 19thInternational Workshop on ADC and DCA Modelling and Testing, IWADC): Understanding the World Through Electrical and Electronic Measurement, Budapest, Hungary. IMEKO, 71-60.

[29] Daponte, P., De Vito, L., Iadarola, G., Rapuano, S. (2016). Effects of PRBS jitter on random demodulation analog-to-information converters. In IEEE Metrology for Aerospace, Florence, Italy. IEEE, 630-635.

[30] Candes, E., Becker, S. (2013). Compressive sensing: Principles and Hardware implementations. In ESSCIRC 2013: 39th European Solid ‐ State Circuits Conference, Bucharest, Romania. IEEE, 22-23.

[31] Wakin, M., Becker, S., Nakamura, E., Grant, M., Sovero, E., Ching, D., Yoo, J. (2012). A non-uniform sampler for wideband spectrally-sparse environments. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2 (3), 516-529.

[32] Faculty of Electrical Engineering and Informatics, Technical University of Košice, Slovakia. (2013-2015). WSN-AQUA Wireless Sensor Network for Water Quality Monitoring (project).

[33] Lopes, M.E. (2013). Estimating unknown sparsity in compressed sensing. In 30thInternational Conference on Machine Learning (ICML 2013), Atlanta, Georgia, USA. International Machine Learning Society (IMLS), 1254-1262.

Measurement Science Review

The Journal of Institute of Measurement Science of Slovak Academy of Sciences

Journal Information


IMPACT FACTOR 2017: 1.345
5-year IMPACT FACTOR: 1.253



CiteScore 2017: 1.61

SCImago Journal Rank (SJR) 2017: 0.441
Source Normalized Impact per Paper (SNIP) 2017: 0.936

Cited By

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 41 41 25
PDF Downloads 31 31 19