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Fast sparse image reconstruction method in through-the-wall radars using limited memory Broyden–Fletcher–Goldfarb–Shanno algorithm

Published online by Cambridge University Press:  16 June 2021

Candida Mwisomba ,
Abdi T. Abdalla Open the ORCID record for Abdi T. Abdalla [Opens in a new window] ,
Idrissa Amour ,
Florian Mkemwa  and
Baraka Maiseli
Candida Mwisomba
Affiliation:
Department of Electronics and Telecommunications Engineering, University of Dar es Salaam, Dar es Salaam, Tanzania
Abdi T. Abdalla*
Affiliation:
Department of Electronics and Telecommunications Engineering, University of Dar es Salaam, Dar es Salaam, Tanzania
Idrissa Amour
Affiliation:
Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania
Florian Mkemwa
Affiliation:
Department of Electronics and Telecommunications Engineering, University of Dar es Salaam, Dar es Salaam, Tanzania
Baraka Maiseli
Affiliation:
Department of Electronics and Telecommunications Engineering, University of Dar es Salaam, Dar es Salaam, Tanzania
*
Author for correspondence: Abdi T. Abdalla, E-mail: [email protected]
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Abstract

Compressed sensing allows recovery of image signals using a portion of data – a technique that has drastically revolutionized the field of through-the-wall radar imaging (TWRI). This technique can be accomplished through nonlinear methods, including convex programming and greedy iterative algorithms. However, such (nonlinear) methods increase the computational cost at the sensing and reconstruction stages, thus limiting the application of TWRI in delicate practical tasks (e.g. military operations and rescue missions) that demand fast response times. Motivated by this limitation, the current work introduces the use of a numerical optimization algorithm, called Limited Memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS), to the TWRI framework to lower image reconstruction time. LBFGS, a well-known Quasi-Newton algorithm, has traditionally been applied to solve large scale optimization problems. Despite its potential applications, this algorithm has not been extensively applied in TWRI. Therefore, guided by LBFGS and using the Euclidean norm, we employed the regularized least square method to solve the cost function of the TWRI problem. Simulation results show that our method reduces the computational time by 87% relative to the classical method, even under situations of increased number of targets or large data volume. Moreover, the results show that the proposed method remains robust when applied to noisy environment.

Keywords

Compressive sensingfast sparse image reconstructionLBFGS algorithmthrough-the-wall radar imaging
Type
Radar
Information
International Journal of Microwave and Wireless Technologies , Volume 14 , Special Issue 6: EuCAP 2020 Special Issue , July 2022 , pp. 739 - 749
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press in association with the European Microwave Association

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References

Amin, MG (2017) Through-the-wall: Radar Imaging. Boca Raton: CRC Press.Google Scholar
Guo, S, Yang, X, Cui, G, Song, Y and Kong, L (2018) Multipath ghost suppression for through-the-wall imaging radar via array rotating. IEEE Geoscience and Remote Sensing Letters 15, 868–872.Google Scholar
Nkwari, PK, Sinha, S and Ferreira, HC (2018) Through-the-wall radar imaging: a review. IETE Technical Review 35, 631–639.Google Scholar
Wu, S, Zhou, H, Liu, S and Duan, R (2020) Improved through-wall radar imaging using modified Green's function-based multi-path exploitation method. EURASIP Journal on Advances in Signal Processing 4, 1–13.Google Scholar
Abdalla, AT, Alkhodary, MT and Muqaibel, AH (2018) Multipath ghosts in through-the-wall radar imaging: challenges and solutions. ETRI Journal 40, 376–388.CrossRefGoogle Scholar
Baranoski, EJ (2008) Through wall imaging: historical perspective and future directions. IEEE International Conference on Acoustics, Speech and Signal Processing – Proceedings, Las Vegas.CrossRefGoogle Scholar
Leigsnering, M, Ahmad, F, Amin, M and Zoubir, A (2014) Multipath exploitation in through-the-wall radar imaging using sparse reconstruction. IEEE Transactions on Aerospace and Electronic Systems 50, 920–939.CrossRefGoogle Scholar
Liu, Q, Gu, Y and So, HC (2019) Smoothed sparse recovery via locally competitive algorithm and forward Euler discretization method. Signal Processing 157, 97–102.CrossRefGoogle Scholar
Yoon, YS and Amin, MG (2008) Compressed sensing technique for high-resolution radar imaging. Signal Processing, Sensor Fusion, and Target Recognition XVII.10.1117/12.777175CrossRefGoogle Scholar
Amin, M and Ahmad, F (2013) Compressive sensing for through-the-wall radar imaging. Journal of Electronic Imaging 22, 030901.CrossRefGoogle Scholar
Donoho, DL (2006) Compressed sensing. IEEE Transactions on Information Theory 54, 1289–1306.CrossRefGoogle Scholar
Candes, EJ and Tao, T (2005) Decoding by linear programming. IEEE Transactions on Information Theory 51, 4203–4215.CrossRefGoogle Scholar
Candes, EJ and Tao, T (2006) Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Transactions on Information Theory 52, 5406–5425.CrossRefGoogle Scholar
Wipf, DP and Rao, BD (2004) Sparse Bayesian learning for basis selection. IEEE Transactions on Signal Processing 52, 2153–2164.CrossRefGoogle Scholar
Liu, Q, Yang, C, Gu, Y and So, HC (2018) Robust sparse recovery via weakly convex optimization in impulsive noise. Signal Processing 152, 84–89.CrossRefGoogle Scholar
Guang, C and Qi, L (2014) Compressed sensing-based angle estimation for noncircular sources in MIMO radar. 4th International Conference on Instrumentation and Measurement, Computer, Communication and Control, Harbin, China.CrossRefGoogle Scholar
Donoho, DL, Tsaig, Y, Drori, I and Starck, JL (2012) Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Transactions on Information Theory 58, 1094–1121.CrossRefGoogle Scholar
Dai, W and Milenkovic, O (2009) Subspace pursuit for compressive sensing signal reconstruction. IEEE Transactions on Information Theory 55, 2230–2249.CrossRefGoogle Scholar
Masood, M and Al-Naffouri, TY (2013) Sparse reconstruction using distribution agnostic Bayesian matching pursuit. IEEE Transactions on Signal Processing 61, 5298–5309.CrossRefGoogle Scholar
Abdalla, AT (2018) Through-the-wall radar imaging with compressive sensing; theory. Practice and Future Trends-A Review. Tanzania Journal of Science 44, 12–30.Google Scholar
Bonnans, J-F, Gilbert, JC, Lemaréchal, C and Sagastizábal, CA (2006) Numerical optimization: theoretical and practical aspects. In Casacuberta, C, Greenlees, J, MacIntyre, A, Sabbah, C, Süli, E and Woyczyński, WA (eds), Numerical Optimization: Theoretical and Practical Aspects. Berlin: Springer, pp. 191–484.Google Scholar
Sun, Y, Chen, L and Qu, L (2019) Through-the-wall radar imaging algorithm for moving target under wall parameter uncertainties. IET Image Processing 13, 1903–1908.CrossRefGoogle Scholar
Muqaibel, AH, Abdalla, AT, Alkhodary, MT and Al-Dharrab, S (2017) Aspect-dependent efficient multipath ghost suppression in TWRI with sparse reconstruction. International Journal of Microwave and Wireless Technologies 9, 1839–1852.CrossRefGoogle Scholar
Abdalla, AT, Muqaibel, AH and Al-dharrab, S (2015) Aspect dependent multipath ghost suppression in twri under compressive sensing framework. Int. Conf. Comm., Sig. Process. and their App., Sharjah.CrossRefGoogle Scholar
AlBeladi, A and Muqaibel, AH (2018) Evaluating compressive sensing algorithms in through-the-wall radar via F1-score. International Journal of Signal and Imaging Systems Engineering 11, 164–171.CrossRefGoogle Scholar
Nocedal, J and Wright, SJ (1999) Numerical Optimization. New York: Springer.CrossRefGoogle Scholar
Broyden, CG (1970) The convergence of a class of double-rank minimization algorithms 1. General considerations. IMA Journal of Applied Mathematics 6, 76–90.CrossRefGoogle Scholar
Matthies, H and Strang, G (1979) The solution of nonlinear finite element equations. International Journal for Numerical Methods in Engineering 14, 1613–1626.CrossRefGoogle Scholar
Nocedal, J and Gilbert, JC (1993) Automatic differentiation and the step computation in the limited memory BFGS method. Applied Mathematics Letters 6, 47–50.Google Scholar
Wei, Z, Li, G and Qi, L (2006) New quasi-Newton methods for unconstrained optimization problems. Applied Mathematics and Computation 175, 1156–1188.CrossRefGoogle Scholar
Xiao, Y, Wei, Z and Wang, ZA (2008) Limited memory BFGS-type method for large-scale unconstrained optimization. Computers and Mathematics with Applications 56, 1001–1009.Google Scholar
Kim, SJ, Koh, K, Lustig, M, Boyd, S and Gorinevsky, D (2007) An interior-point method for large-scale ℓ1-regularized least squares. IEEE Journal on Selected Topics in Signal Processing 1, 606–617.CrossRefGoogle Scholar
Figueiredo, MAT, Nowak, RD and Wright, SJ (2007) Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE Journal on Selected Topics in Signal Processing 1, 586–597.CrossRefGoogle Scholar
Calvetti, D, Morigi, S, Reichel, L and Sgallari, F (2000) Tikhonov regularization and the L-curve for large discrete ill-posed problems. Journal of Computational and Applied Mathematics 123, 423–446.CrossRefGoogle Scholar
Golub, GH, Hansen, PC and O'Leary, DP (1999) Tikhonov regularization and total least squares. SIAM Journal on Matrix Analysis and Applications 21, 185–194.CrossRefGoogle Scholar
Kokumo, E, Abdalla, A and Maiseli, B (2019) Target-to-target interaction in through-the-wall radars under path-loss compensated multipath exploitation-based signal model for sparse image reconstruction. Tanzania Journal of Science 45, 382–391.Google Scholar