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Recent Advances in Electrical & Electronic Engineering

Author(s): Deepak M. Devendrappa*, Karthik Palani and Deepak N. Ananth

DOI: 10.2174/2352096516666221202104912

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Analysis of Sparse Signal Sequences under Compressive Sampling Techniques for Different Measurement Matrices

Page: [472 - 485] Pages: 14

  • * (Excluding Mailing and Handling)

Abstract

Introduction: A more modern, extremely applicable method for signal acquisition is compression sensing. It permits effective data sampling at a rate that is significantly lower than what the Nyquist theorem suggests. Compressive sensing has a number of benefits, including a muchreduced demand for sensory devices, a smaller memory storage need, a greater data transfer rate, and significantly lower power usage. Compressive sensing has been employed in a variety of applications because of all these benefits. Neuro-signal acquisition is a domain in which compressive sensing has applications in the medical industry.

Methods: The novel methods discussed in this article are FFT-based CoSaMP (FFTCoSaMP), DCT-based CoSaMP(DCTCoSaMP) and DWT-based CoSaMP (DWTCoSaMP) based on sparse signal sequences / dictionaries by means of Transform Techniques, where CoSaMP stands for Compressive Sampling Matching Pursuit with respect to Objective Quality Assessment Algorithms like PSNR, SSIM and RMSE, where CoSaMP stands for Compressive Sampling Matching Pursuit.

Results: DWTCoSaMP is giving the PSNR values of 40.26 db, for DCTCoSaMP and FFTCoSaMP, PSNR is 36.76 db and 34.76 db. For DWTCoSaMP, SSIM value is 0.8164, and for DCTCoSaMP and FTCoSaMP, SSIM 0.719 and 0.5625 respectively. Finally, for DWTCoSaMP, RMSE value is 0.442, and for DCTCoSaMP and FFTCoSaMP, SSIM 0.44 and 0.4425, respectively.

Conclusion: Among Compressed sampling techniques DWTCoSaMP, DCTCoSaMP and FFTCoSaMP discussed in this paper, DWTCoSaMP reveals the best results.

Graphical Abstract

[1]
D.L. Donoho, "Compressed sensing", IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, 2006.
[http://dx.doi.org/10.1109/TIT.2006.871582]
[2]
G. Yang, S. Yu, H. Dong, G. Slabaugh, P.L. Dragotti, X. Ye, F. Liu, S. Arridge, J. Keegan, Y. Guo, D. Firmin, J. Keegan, G. Slabaugh, S. Arridge, X. Ye, Y. Guo, S. Yu, F. Liu, D. Firmin, P.L. Dragotti, G. Yang, and H. Dong, "DAGAN: deep de-aliasing generative adversarial networks for fast compressed sensing MRI reconstruction", IEEE Trans. Med. Imaging, vol. 37, no. 6, pp. 1310-1321, 2018.
[http://dx.doi.org/10.1109/TMI.2017.2785879] [PMID: 29870361]
[3]
D.L. Donoho, M. Elad, and V.N. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise", IEEE Trans. Inf. Theory, vol. 52, no. 1, pp. 6-18, 2006.
[http://dx.doi.org/10.1109/TIT.2005.860430]
[4]
M. Lustig, D. Donoho, and J.M. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging", Magn. Reson. Med., vol. 58, no. 6, pp. 1182-1195, 2007.
[http://dx.doi.org/10.1002/mrm.21391] [PMID: 17969013]
[5]
S.G. Mallat, and Zhifeng Zhang, "Matching pursuits with time-frequency dictionaries", IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3397-3415, 1993.
[http://dx.doi.org/10.1109/78.258082]
[6]
B.M.J.S.M.Z.M. Elad, "A Wide-angle view at iterated shrinkage algorithms", Proc. SPIE Optics Photonics: Wavelets, San Diego, California, United States, 2007.
Available from: https://www.spiedigitallibrary.org/conference-proceedings-ofspie/ 6701/1/A-wide-angle-view-at-iterated-shrinkagealgorithms/ 10.1117/12.741299.full?SSO=1 [http://dx.doi.org/10.1117/12.741299]
[7]
D. Needell, and J.A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples", Appl. Comput. Harmon. Anal., vol. 26, no. 3, pp. 301-321, 2009.
[http://dx.doi.org/10.1016/j.acha.2008.07.002]
[8]
B. Li, F. Liu, C. Zhou, Y. Lv, and J. Hu, "Phase error correction for approximated observation-based compressed sensing radar imaging", Sensors, vol. 17, no. 3, p. 613, 2017.
[http://dx.doi.org/10.3390/s17030613] [PMID: 28304353]
[9]
H.J. Landau, "Sampling, data transmission, and the Nyquist rate", Proc. IEEE, vol. 55, no. 10, pp. 1701-1706, 1967.
[http://dx.doi.org/10.1109/PROC.1967.5962]
[10]
E.J. Candès, and M.B. Wakin, "An Introduction To Compressive Sampling", IEEE Signal Process. Mag., vol. 2, no. 5, pp. 21-30, 2008.
[11]
E.J. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information", IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, 2006.
[http://dx.doi.org/10.1109/TIT.2005.862083]
[12]
N. Ahmed, T. Natarajan, and K.R. Rao, "Discrete cosine transform", IEEE Trans. Comput., vol. C-23, no. 1, pp. 90-93, 1974.
[http://dx.doi.org/10.1109/T-C.1974.223784]
[13]
J.W. Cooley, P.A.W. Lewis, and P.D. Welch, "The Fast Fourier Transform and Its Applications", IEEE Trans. Educ., vol. 12, no. 1, pp. 27-34, 1969.
[http://dx.doi.org/10.1109/TE.1969.4320436]
[14]
S. Mallat, and S. Zhong, "Characterization of signals from multiscale edges", IEEE Trans. Pattern Anal. Mach. Intell., vol. 14, no. 7, pp. 710-732, 1992.
[http://dx.doi.org/10.1109/34.142909]
[15]
W.S.A.I.S.A.N. Akansu, Wavelet Transforms in Signal Processing: A Review of Emerging Applications, Physical Communication., vol. 3. Elsevier, 2010, no. 1, pp. 1-18.
[16]
Z. Wu, J. Sha, Z. Wang, L. Li, and M. Gao, "An improved scaled DCT architecture", IEEE Trans. Consum. Electron., vol. 55, no. 2, pp. 685-689, 2009.
[http://dx.doi.org/10.1109/TCE.2009.5174440]
[17]
P. Heckbert, "Fourier Transforms and the Fast FourierTransform (FFT) Algorithm", Comput. Graph., vol. 2, pp. 15-463, 1998.
[18]
J.D. Villasenor, B. Belzer, and J. Liao, "Wavelet filter evaluation for image compression", IEEE Trans. Image Process., vol. 4, no. 8, pp. 1053-1060, 1995.
[http://dx.doi.org/10.1109/83.403412] [PMID: 18291999]
[19]
Harry Nyquist, "Certain topics in telegraph transmission theory", Trans. AIEE., vol. 47, no. 2, pp. 617-644, 1928.
[http://dx.doi.org/10.1109/T-AIEE.1928.5055024]
[20]
Ying Chen, Shuai Liu, Xu-Ri Yao, Qing Zhao, Xue-Feng Liu, Bing Liu, and Guang-Jie Zhai, Discrete cosine single-pixel microscopic compressive imaging via fast binary modulation, Optics Communications, Volume 454, 2020.
[21]
J.F.K. Kenney, "Root Mean Square", In: NJ. Van Nostrand, Ed., Mathematics of Statistics., Princeton, 1962, pp. 59-60.
[22]
A. Wahid, J.A. Shah, A.U. Khan, M. Ahmed, and H. Razali, "Multi-layer basis pursuit for compressed sensing MR image reconstruction", IEEE Access, vol. 8, pp. 186222-186232, 2020.
[http://dx.doi.org/10.1109/ACCESS.2020.3028877]
[23]
R.S. Mathew, and J.S. Paul, "Automated regularization parameter selection using continuation based proximal method for compressed sensing MRI", IEEE Trans. Comput. Imaging, vol. 6, pp. 1309-1319, 2020.
[http://dx.doi.org/10.1109/TCI.2020.3019111]
[24]
C.M. Sandino, J.Y. Cheng, F. Chen, M. Mardani, J.M. Pauly, and S.S. Vasanawala, "Compressed sensing: from research to clinical practice with deep neural networks: Shortening Scan Times for Magnetic Resonance Imaging", IEEE Signal Process. Mag., vol. 37, no. 1, pp. 117-127, 2020.
[http://dx.doi.org/10.1109/MSP.2019.2950433] [PMID: 33192036]
[25]
F. Zong, J. Du, X. Deng, X. Chai, Y. Zhuo, A.V. Vegh, and R. Xue, "Fast Diffusion Kurtosis Mapping of Human Brain at 7 Tesla With Hybrid Principal Component Analyses", IEEE Access, vol. 9, pp. 107965-107975, 2021.
[http://dx.doi.org/10.1109/ACCESS.2021.3100546]
[26]
Y. Han, L. Sunwoo, and J. C. Ye, "${k}$ -Space Deep Learning for Accelerated MRI", IEEE Transactions on Medical Imaging, vol. 39, no. 2, pp. 377-386, 2020.
[http://dx.doi.org/10.1109/TMI.2019.2927101]
[27]
B.P.V. Dileep, T. Das, and P.K. Dutta, "Greedy algorithms for diffuse optical tomography reconstruction", Opt. Commun., vol. 410, pp. 164-173, 2018.
[http://dx.doi.org/10.1016/j.optcom.2017.09.056]
[28]
B.P.V. Dileep, P.K. Dutta, P.M.K. Prasad, and M. Santhosh, "Sparse recovery based compressive sensing algorithms for diffuse optical tomography", Opt. Laser Technol., vol. 128, p. 106234, 2020.
[http://dx.doi.org/10.1016/j.optlastec.2020.106234]
[29]
F. Kong, "Comparison of reconstruction algorithm for compressive sensing magnetic resonance imaging", Multimed Tools Appl 77, pp. 22617-22628, 2018.
[http://dx.doi.org/10.1007/s11042-017-4985-2]
[30]
Amira S. Ashour, Yanhui Guo, Eman Elsaid Alaa, and Hossam M. Kasem, "Discrete cosine transform–based compressive sensing recovery strategies in medical imaging", Advances in Computational Techniques for Biomedical Image Analysis, Academic Press, pp. 167-184, 2020.
[31]
Gao Y-F., Cong X-C., Yang Y., Wan Q., and Gui G., A Tensor Decomposition Based Multiway Structured Sparse SAR Imaging Algorithm with Kronecker Constraint. Algorithms
2017, 10, 2. [http://dx.doi.org/10.3390/a10010002]
[32]
H. Ahmed, and A.K. Nandi, Compressive Sampling and Feature Ranking Framework for Bearing Fault Classification With Vibration Signals., vol. 6. IEEE, 2018.
[33]
B.B.Y.Z.A.P.H. Peng, "Sparse reconstruction off-grid OFDM time delay estimation algorithm based on bayesian automatic relevance de-termination", Journal of Physics, IOP Science, vol. 1237, no. 2, 2019.
[34]
S. Anitha, L. Kola, P. Sushma, and S. Archana, "Analysis of Filtering and Novel Technique for Noise Removal in MRI and CT Images", International Conference on Electrical, Electronics, Communication, Computer and Optimization Techniques (ICEECCOT), Dec 15-16, 2017, Mysuru, pp. 1-3, 2017.
[http://dx.doi.org/10.1109/ICEECCOT.2017.8284618]
[35]
X. Li, W. Wang, S. Zhu, W. Xiang, and X. Wu, "Generalized nesterov accelerated conjugate gradient algorithm for a compressively sampled MR imaging reconstruction", IEEE Access, vol. 8, pp. 157130-157139, 2020.
[http://dx.doi.org/10.1109/ACCESS.2020.3018446]
[36]
G. Li, J. Lv, and C. Wang, "A modified generative adversarial network using spatial and channel-wise attention for CS-MRI reconstruction", IEEE Access, vol. 9, pp. 83185-83198, 2021.
[http://dx.doi.org/10.1109/ACCESS.2021.3086839]
[37]
Z.H. Xie, L.J. Liu, X.Y. Wang, and C. Yang, "An iterative method with enhanced laplacian- scaled thresholding for noise-robust compressive sensing magnetic resonance image reconstruction", IEEE Access, vol. 8, pp. 177021-177040, 2020.
[http://dx.doi.org/10.1109/ACCESS.2020.3027313]
[38]
Y. Liu, and Q. Liu, "IFR-Net: Iterative Feature Refinement Network for Compressed Sensing MRI, Issue 7", IEEE Trans. Comput. Imaging, vol. 1, no. 1, p. 99, 2019.
[39]
M. Khosravy, N. Gupta, N. Patel, and C.A. Duque, "Recovery in compressive sensing: a review", In: Advances in ubiquitous sensing applications for healthcare., 2020.
[http://dx.doi.org/10.1016/B978-0-12-821247-9.00007-X]
[40]
Z. Meng, G. Zhang, Z. Pan, W. Gao, H. Gao, and F. Fan, "A sparse measurement matrix based method for feature enhancement of bearing fault signal", Appl. Acoust., vol. 177, p. 107903, 2020.
[http://dx.doi.org/10.1016/j.apacoust.2020.107903]
[41]
D.N.A.D.M.D.P. Karthik, "Comparative study of feature extraction using different transform techniques in frequency domain", In: Automation, Signal Processing, Instrumentation, Lecture Notes in Electrical Engineering Springer., Springer, 2021, pp. 2835-2846.
[42]
I.D. Irawati, S. Hadiyoso, and Y.S. Hariyani, "Multi-wavelet level comparison on compressive sensing for MRI image reconstruction. Bull. Electric", Engin. Inform., vol. 9, no. 4, pp. 1461-1467, 2020.
[http://dx.doi.org/10.11591/eei.v9i4.2347]
[43]
P.K. Pokala, S. Chemudupati, and C.S. Seelamantula, "Generalized fast iteratively reweighted soft-thresholding algorithm for sparse coding under tight frames in the complex-domain", Proceedings - International Conference on Image Processing, IEEE Computer Society, Oct 25-28, 2020: Abu Dhabi, United Arab Emirates, pp. 2875-2879, 2020.
[http://dx.doi.org/10.1109/ICIP40778.2020.9190686]