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ISSN: 1023-5086

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ISSN: 1023-5086

Scientific and technical

Opticheskii Zhurnal

A full-text English translation of the journal is published by Optica Publishing Group under the title “Journal of Optical Technology”

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DOI: 10.17586/1023-5086-2022-89-05-31-40

УДК: 004.93, 681.772, 681.7.013

Image reconstruction based on a single-pixel camera and left optimization

For Russian citation (Opticheskii Zhurnal):

Cheng T., Li D.G. Реконструкция изображения на основе однопикселной камеры и левосторонней оптимизации. Image reconstruction based on a single-pixel camera and left optimization  [на англ. яз.] // Оптический журнал. 2022. Т. 89. № 5. С. 31–40. http://doi.org/10.17586/1023-5086-2022-89-05-31-40

 

Cheng T., Li D.G. Реконструкция изображения на основе однопикселной камеры и левосторонней оптимизации. Image reconstruction based on a single-pixel camera and left optimization [in English] // Opticheskii Zhurnal. 2022. V. 89. № 5. P. 31–40. http://doi.org/10.17586/1023-5086-2022-89-05-31-40

For citation (Journal of Optical Technology):

Tao Cheng and Degao Li, "Image reconstruction based on a single-pixel camera and left optimization," Journal of Optical Technology. 89(5), 269-276 (2022). https://doi.org/10.1364/JOT.89.000269

Abstract:

Subject of study. A set of schemes that can make the single-pixel camera use the prior information of the image to improve the image reconstruction effect is proposed. Method. After the measurement data of the single-pixel camera is processed by standardization or left optimization, the energy and direction information of the signal can be reflected by the processed data. According to the energy and direction information characteristics of the reconstructed image by orthogonal matching pursuit, the use of total variation minimization algorithms in specific area can improve the image reconstruction effect. Main Results. Based on the [0-1] random matrix and the [0-1] circulant matrix, the measurement data of the single-pixel camera cannot effectively reflect the energy and direction information of the signal. After the measurement data of a single-pixel camera are processed by standardization, the energy information of the signal can be more clearly reflected. Although the direction information is also reflected, it is not very obvious. After the measurement data of the single-pixel camera are processed by left optimization, both the energy and direction information of the signal can be well reflected. Therefore, the energy and direction information of the measurement data of the singlepixel camera after left optimization can be used as criteria for evaluating the quality of the signal reconstruction. Experimental results show that based on such criteria, using orthogonal matching pursuit and total variation minimization algorithms in different columns of the measurement data can greatly improve the image reconstruction. Even if the measurement data contains noise, signal-to-noise ratio can be improved by more than 16 dB. Practical significance. In real compressed sensing engineering applications, the measurement data and measurement matrix are the only known factors. Because the real image is unknown, the quality of the reconstruction can only be evaluated based on long-term work experience. Or logical reasoning is on basis of the results of simulation experiments. Based on the energy and direction information of the measurement data of the single-pixel camera after left optimization, the result of image reconstruction can be evaluated objectively.

Keywords:

single-pixel camera, compressed sensing, measurement matrix, standardization, left optimization, image reconstruction

Acknowledgements:

The work is supported by the National Natural Science Foundation of China under Grants 41461082 and 81660296 and the China Postdoctoral Science  Foundation under Grant 2016M592525.

OCIS codes: 200.0200, 100.3010

References:

1. Donoho D.L. Compressed sensing // IEEE Trans. Inf. Theory. 2006. V. 52. № 4. P. 1289–1306.
2. Duarte-Carvajalino J.M., Sapiro G. Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization // IEEE Trans. Image Process. 2009. V. 18. № 7. P. 1395–1408.
3. Elad M. Optimized projections for compressed sensing // IEEE Trans. Signal Process. 2007. V. 55. № 12. P. 5695–5702.
4. Cheng T., Chen D., Yu B., et al. Reconstruction of super-resolution STORM images using compressed sensing based on low-resolution raw images and interpolation // Biomedical Opt. Exp. 2017. V. 8. № 5. P. 2445–2457.
5. Zhu L., Zhang W., Elnatan D., et al. Faster STORM using compressed sensing // Nat. Methods. 2010. V. 9. № 7. P. 721–723.
6. Cheng T. Reconstruction improvement of single-pixel camera based on operator matrix-induced compressive sensing // J. Geod. List. 2020. V. 41(03). P. 283–296.
7. Joy A., Paul J.S. A mixed-order nonlinear diffusion compressed sensing MR image reconstruction // Magn. Reson. Med. 2017. V. 80. № 5. P. 2215–2222.
8. Jin K.H., Um J.-Y., Lee D., et al. MRI artifact correction using sparse plus low-rank decomposition of annihilating filter-based hankel matrix // Magn. Reson. Med. 2016. V. 78. № 1. P. 327–340.
9. Das S., Mandal J.K. An enhanced block-based compressed sensing technique using orthogonal matching pursuit // Signal Image Video Process. 2019. V. 15. № 3. P. 563–570.
10. Lee K., Yu N.Y. Exploiting prior information for greedy compressed sensing based detection in machinetype communications // Digit. Signal Process. 2018. V. 107. № 12. P. 1–12.
11. Bredies K., Holler M. Higher-order total variation approaches and generalisations // Inverse Probl. 2019. V. 36. № 12. P. 1–128.
12. Vishnukumar S., Wilscy M. Single image super-resolution based on compressive sensing and improved TV minimization sparse recovery // Opt. Commun. 2017. V. 404. № 23. P. 80–93.
13. Qin S. Simple algorithm for L1-norm regularisation-based compressed sensing and image restoration // IET Image Process. 2021. V. 14. № 14. P. 3405–3413.
14. Thuong Nguyen C., Jeon B. Restricted structural random matrix for compressive sensing // Signal Process. Image Commun. 2021. V. 90. № 1. P. 1–14.
15. Nouasria H., Et-Tolba M. A new efficient sensing matrix for cluster structured sparse signals recovery // Digit. Signal Process. 2019. V. 92. № 9. P. 166–178.
16. Lotz M. Persistent homology for low-complexity models // Proc. Math. Phys. Eng. 2019. V. 475. № 2230. P. 1–21. 17. Cheng T. Restricted conformal property of compressive sensing // 11th Int. Comput. Conf. Wavelet Act. 2014. P. 152–161.
18. Cheng T. Directional remote sensing // Geod. List. 2015. V. 36 № 04. P. 251–262.
19. Shaeiri Z., Karami M.-R., Aghagolzadeh A. Enhancing the fundamental limits of sparsity pattern recovery // Digit. Signal Process. 2017. V. 69. № 10. P. 275–285.
20. Sasmal P., Murthy C.R. Incoherence is sufficient for statistical RIP of unit norm tight frames: Constructions and properties // IEEE Trans. Signal Process. 2021. V. 69. № 1. P. 2343–2355.