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Efficient Spatially-Variant Single-Pixel Imaging Using Block-Based Compressed Sensing

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Abstract

Single-pixel imaging is an important alternative to conventional camera. Only a single-pixel detector is needed to capture image data by measuring the correlation of the target scene and a series of sensing patterns. Conventionally, Nyquist-Shannon theorem requires measurements not less than the image pixels for an error-free reconstruction. Compressed sensing (CS) enables image reconstructions with fewer measurements but the image quality and computational cost remain the primary concerns. This paper presents an efficient single-pixel imaging technique based on blocked-based CS in which the sensing matrices are designed based on spatially-variant resolution (SVR). The proposed method decreases the number of measurements as well as the image reconstruction time using the SVR sensing patterns. Furthermore, it takes advantage of block-based CS to reduce the expenses of computational resources. The proposed method is evaluated and compared to conventional uniform resolution (UR) image reconstruction in terms of image quality and reconstruction time. The results show that the proposed method consistently reduces the reconstruction time and able to give better image quality at lower sampling ratio (SR). This provides an efficient reconstruction for single-pixel imaging which is desirable in practical application and situations where low sampling rate is required.

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Notes

  1. The code of TVAL3 used in this paper can be found on https://github.com/larzw/TVAL3.

References

  1. Baraniuk, R. G. (2007). Compressive sensing [lecture notes]. IEEE signal processing magazine, 24(4), 118–121.

  2. Bian, L., Suo, J., Situ, G., Li, Z., Fan, J., Chen, F., & Dai, Q. (2016). Multispectral imaging using a single bucket detector. Scientific reports, 6(1), 1–7.

  3. Bigot, J., Boyer, C., & Weiss, P. (2016). An analysis of block sampling strategies in compressed sensing. IEEE transactions on information theory, 62(4), 2125–2139.

  4. Bo L., Lu, H., Lu, Y., Meng J., Wang, W. (2017). Fompnet: Compressive sensing reconstruction with deep learning over wireless fading channels. In: 2017 9th International Conference on Wireless Communications and Signal Processing (WCSP), IEEE, pp 1–6

  5. Candes, E. J., & Tao, T. (2006). Near-optimal signal recovery from random projections: Universal encoding strategies? IEEE transactions on information theory, 52(12), 5406–5425.

  6. Candès, E. J., & Wakin, M. B. (2008). An introduction to compressive sampling. IEEE signal processing magazine, 25(2), 21–30.

  7. Candès, E. J., et al. (2006). Compressive sampling. Proceedings of the international congress of mathematicians, Madrid, Spain, 3, 1433–1452.

  8. Canh, T. N., & Jeon, B. (2021). Restricted structural random matrix for compressive sensing. Signal Processing: Image Communication, 90.

  9. Chua, S. Y., Guo, N., Tan, C. S., & Wang, X. (2017). Improved range estimation model for three-dimensional (3d) range gated reconstruction. Sensors, 17(9), 2031.

  10. Czajkowski, K. M., Pastuszczak, A., & Kotyński, R. (2018). Real-time single-pixel video imaging with fourier domain regularization. Optics express, 26(16), 20009–20022.

  11. Dabov, K., Foi, A., Katkovnik, V., & Egiazarian, K. (2007). Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Transactions on image processing, 16(8), 2080–2095.

  12. Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on information theory, 52(4), 1289–1306.

  13. Donoho, D. L., Maleki, A., & Montanari, A. (2009). Message-passing algorithms for compressed sensing. Proceedings of the National Academy of Sciences, 106(45), 18914–18919.

  14. Duarte, M. F., Davenport, M. A., Takhar, D., Laska, J. N., Sun, T., Kelly, K. F., & Baraniuk, R. G. (2008). Single-pixel imaging via compressive sampling. IEEE signal processing magazine, 25(2), 83–91.

  15. Edgar, M. P., Gibson, G. M., Bowman, R. W., Sun, B., Radwell, N., Mitchell, K. J., et al. (2015). Simultaneous real-time visible and infrared video with single-pixel detectors. Scientific reports, 5(1), 1–8.

  16. Fan, K., Suen, J. Y., & Padilla, W. J. (2017). Graphene metamaterial spatial light modulator for infrared single pixel imaging. Optics express, 25(21), 25318–25325.

  17. Gan, H., Xiao, S., Zhao, Y., & Xue, X. (2018). Construction of efficient and structural chaotic sensing matrix for compressive sensing. Signal Processing: Image Communication, 68, 129–137.

  18. Gan, H., Xiao, S., Zhang, T., Zhang, Z., Li, J., & Gao, Y. (2019). Chaotic pattern array for single-pixel imaging. Electronics, 8(5), 536.

  19. Gan, L. (2007). Block compressed sensing of natural images. In: 2007 15th International conference on digital signal processing, IEEE, pp 403–406

  20. Gattinger, P., Kilgus, J., Zorin, I., Langer, G., Nikzad-Langerodi, R., Rankl, C., et al. (2019). Broadband near-infrared hyperspectral single pixel imaging for chemical characterization. Optics express, 27(9), 12666–12672.

  21. Gibson, G. M., Johnson, S. D., & Padgett, M. J. (2020). Single-pixel imaging 12 years on: a review. Optics Express, 28(19), 28190–28208.

  22. Guo, Q., Yx, Wang, Hw, Chen, Chen, Mh., Sg, Yang, & Sz, Xie. (2017). Principles and applications of high-speed single-pixel imaging technology. Frontiers of Information Technology & Electronic Engineering, 18(9), 1261–1267.

  23. Hayashi, K., Nagahara, M., & Tanaka, T. (2013). A user’s guide to compressed sensing for communications systems. IEICE transactions on communications, 96(3), 685–712.

  24. Howland, G.A., Dixon, P.B., Howell, J.C. (2011). Photon-counting compressive sensing laser radar for 3d imaging. Applied Optics, 50(31):5917–5920.

  25. Howland, G.A., Lum, D.J., Ware, M.R., Howell, J.C. (2013). Photon counting compressive depth mapping. Optics express, 21(20):23822–23837.

  26. Kulkarni K., Lohit S., Turaga P., Kerviche R., Ashok A. (2016) Reconnet: Non-iterative reconstruction of images from compressively sensed measurements. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp 449–458

  27. Li, C., Yin, W., Jiang, H., & Zhang, Y. (2013). An efficient augmented lagrangian method with applications to total variation minimization. Computational Optimization and Applications, 56(3), 507–530.

  28. Lin, Y. M., Zhang, J. F., Geng, J., & Wu, A. Y. A. (2018). Structural scrambling of circulant matrices for cost-effective compressive sensing. Journal of Signal Processing Systems, 90(5), 695–707.

  29. Lu, H., & Bo, L. (2019). Wdlreconnet: Compressive sensing reconstruction with deep learning over wireless fading channels. IEEE Access, 7, 24440–24451.

  30. Lu, T., Qiu, Z., Zhang, Z., & Zhong, J. (2020). Comprehensive comparison of single-pixel imaging methods. Optics and Lasers in Engineering, 134,.

  31. Magalhães, F., Araújo, F.M., Correia, M.V., Abolbashari, M., Farahi, F. (2011). Active illumination single-pixel camera based on compressive sensing. Applied Optics, 50(4):405–414.

  32. Mathai, A., Wang, X., Chua, S.Y. (2019). Transparent object detection using single-pixel imaging and compressive sensing. In: 2019 13th International Conference on Sensing Technology (ICST), IEEE, pp 1–6

  33. Mun, S., Fowler, J.E. (2009) Block compressed sensing of images using directional transforms. In: 2009 16th IEEE international conference on image processing (ICIP), IEEE, pp 3021–3024

  34. Nguyen, T.L., Shin, Y. (2013). Deterministic sensing matrices in compressive sensing: a survey. The Scientific World Journal 2013.

  35. Phillips, D. B., Sun, M. J., Taylor, J. M., Edgar, M. P., Barnett, S. M., Gibson, G. M., & Padgett, M. J. (2017). Adaptive foveated single-pixel imaging with dynamic supersampling. Science advances, 3(4).

  36. Rousset, F., Ducros, N., Peyrin, F., Valentini, G., Dandrea, C., & Farina, A. (2018). Time-resolved multispectral imaging based on an adaptive single-pixel camera. Optics express, 26(8), 10550–10558.

  37. Shi, W., Jiang, F., Liu, S., & Zhao, D. (2019). Image compressed sensing using convolutional neural network. IEEE Transactions on Image Processing, 29, 375–388.

  38. Shin, Z., Lin, H. S., Chai, T. Y., Wang, X., & Chua, S. Y. (2021). Programmable spatially variant single-pixel imaging based on compressive sensing. Journal of Electronic Imaging, 30(2), 1–15.

  39. Shin, Z.Y., Lin, H.S., Chai, T.Y., Wang, X., Chua, S.Y. (2019). Programmable single-pixel imaging. In: 2019 13th International Conference on Sensing Technology (ICST), IEEE, pp 1–6

  40. Stantchev, R. I., Sun, B., Hornett, S. M., Hobson, P. A., Gibson, G. M., Padgett, M. J., & Hendry, E. (2016). Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector.Science advances, 2(6).

  41. Sun, B., Edgar, M. P., Bowman, R., Vittert, L. E., Welsh, S., Bowman, A., & Padgett, M. J. (2013). 3d computational imaging with single-pixel detectors. Science, 340(6134), 844–847.

  42. Sun, M. J., & Zhang, J. M. (2019). Single-pixel imaging and its application in three-dimensional reconstruction: a brief review. Sensors, 19(3), 732.

  43. Sun, M. J., Meng, L. T., Edgar, M. P., Padgett, M. J., & Radwell, N. (2017). A russian dolls ordering of the hadamard basis for compressive single-pixel imaging. Scientific reports, 7(1), 1–7.

  44. Vaz, P. G., Amaral, D., Ferreira, L. R., Morgado, M., & Cardoso, J. (2020). Image quality of compressive single-pixel imaging using different hadamard orderings. Optics express, 28(8), 11666–11681.

  45. Wei, J., Huang, Y., Lu, K., & Wang, L. (2017). Fields of experts based multichannel compressed sensing. Journal of Signal Processing Systems, 86(2–3), 111–121.

  46. Ye, Z., Wang, H., Xiong, J., & Wang, K. (2020). Simultaneous full-color single-pixel imaging and visible watermarking using hadamard-bayer illumination patterns. Optics and Lasers in Engineering 127,.

  47. Yu, X., Stantchev, R. I., Yang, F., & Pickwell-MacPherson, E. (2020). Super sub-nyquist single-pixel imaging by total variation ascending ordering of the hadamard basis. Scientific Reports, 10(1), 1–11.

  48. Yuan, A. Y., Feng, J., Jiao, S., Gao, Y., Zhang, Z., Xie, Z., et al. (2021). Adaptive and dynamic ordering of illumination patterns with an image dictionary in single-pixel imaging. Optics Communications, 481.

  49. Zhang, Y., Edgar, M. P., Sun, B., Radwell, N., Gibson, G. M., & Padgett, M. J. (2016). 3d single-pixel video. Journal of Optics, 18(3).

  50. Zhang, Y., Huang, Y., Li, H., Li, P., Fan, X., et al. (2019). Conjugate gradient hard thresholding pursuit algorithm for sparse signal recovery. Algorithms, 12(2), 36.

  51. Zhao, M., Liu, J., Chen, S., Kang, C., Xu W. (2015). Single-pixel imaging with deterministic complex-valued sensing matrices. Journal of the European Optical Society-Rapid publications 10

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Acknowledgements

The authors gratefully acknowledge the support of funding from UTAR Research Fund (UTARRF) under the Project No. IPSR/RMC/UTARRF/2020-C2/C07, Vote No. 6200/CH6.

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Correspondence to Sing Yee Chua.

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Shin, Z., Chai, TY., Pua, C.H. et al. Efficient Spatially-Variant Single-Pixel Imaging Using Block-Based Compressed Sensing. J Sign Process Syst 93, 1323–1337 (2021). https://doi.org/10.1007/s11265-021-01689-5

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