Presenting a new method to separate fetal heart signals from the mother by using sequential quadratic programming

Document Type : Original Paper


Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran


One of the most common causes of death during the birth of babies is heart failure. Diagnosis of this disease requires observation of heart activity. Since the electrical signals recorded in the mother’s abdomen contain a lot of information such as: mother’s heart signal, mother’s and fetus’s muscle activity, fetus’s brain activity and environmental noises, researchers are looking for ways to separate the fetus’s heart signals from the mother’s are. The proposed method has super-linear convergence, which provides global convergence results and an exact solution to solve the sub-problem. The performance of the proposed method is compared with the best existing methods and the results show that the proposed method has the lowest error rate and the highest speed in separating fetal heart signals from the mother compared to other methods.


Main Subjects

[1] L. U. O. Zhongliang, Fetal electrocardiogram extraction using blind source separation and empirical mode decomposition, Journal of Computational Information Systems, 8 (2012) 4825–4833.
[2] B. A. Olshausen and D. J. Field, Sparse coding with an overcomplete basis set: A strategy employed by V1?, Vision research, 37 (1997) 3311–3325.
[3] R. G. Baraniuk, Compressive sensing [lecture notes], IEEE signal processing magazine, 24 (2007) 118–121.
[4] R. Liu, W. Cai, G. Li, X. Ning and Y. Jiang, Hybrid dilated convolution guided feature filtering and enhancement strategy for hyperspectral image classification, IEEE Geoscience and Remote Sensing Letters, 19 (2021) 1–5.
[5] M. S. Alamdari, M. Fatemi and A. Ghaffari, A Modified Sequential Quadratic Programming Method for Sparse Signal Recovery Problems, Signal Processing, (2023) 108955.
[6] A. M. Bruckstein, D. L. Donoho, and M. Elad, From sparse solutions of systems of equations to sparse modeling of signals and images, SIAM Rev. 51 (2009) 34–81.
[7] R. Liu, M. Shu, and C. Chen, ECG Signal Denoising and Reconstruction Based on Basis Pursuit, Applied Sciences, 4 (2021) 1591.
[8] W. Jinming and L. Haifeng, Binary sparse signal recovery with binary matching pursuit, Inverse Problems, 37 (2021) 14–65.
[9] C. Xueping Chen, L. Jianzhong and C. Jiandong, A new result on recovery sparse signals using orthogonal matching pursuit, Statistical Theory and Related Fields, (2022) 1–7.
[10] H. Mohimani, M. Babaie-Zadeh, and C. Jutten, A fast approach for overcomplete sparse decomposition based on smoothed ℓ0 norm, IEEE Trans. Signal processing, 57 (2009) 289–301.
[11] R.B. Wilson, A simplical algorithm for concave programming (Ph.D.thesis), Harvard University Graduate School of Business Administration, (1963).
[12] S.P. Han, A globally convergent method for nonlinear programming, J.Optim. Theory Apply, 22 (1977) 297–309.
[13] M.J.D. Powell, A fast algorithm for nonlinearly constrained optimization calculations, in: G.A. Watson (Ed.), Numerical Analysis, Springer-Verlag, Berlin, (1978) 144–157.
[14] R. Fletcher, S. Leyffer, and P. L. Toint, On the Global Convergence of a Filter-SQP Algorithm, Technical Report 15, Department of Mathematics, University of Namur, Namur, Belgium, (2000).
[15] R. Fletcher, The Sequential Quadratic Programming, Method Nonlinear optimization, Lecture Note in mathematics, (2010) 165–214.
[16] D. Malioutov and A. Aravkin, Iterative log thresholding, in IEEE Int.Conf. Acoust. Speech Signal Processing, (2014).
[17] S. Foucart and M. Lai, Sparsest solutions of under-determined linear systems via ellq-minimization for 0 < q ≤ 1, Appl. Comput. Harmon. Anal, 26 (2009) 395–407.
[18] A. Eftekhari, M. Babaie-Zadeh, C. Jutten, and H. Abrishami Moghaddam, Robust-SL0 for stable sparse representation in noisy settings, in IEEE Int. Conf. Acoust. Speech Signal Processing, (2009) 3433–3436.
[19] A. Belloni, V. Chernozhukov, and L. Wang, Square-root lasso: pivotal recovery of sparse signals via conic programming, Biometrika, 98 (2011) 791–806.
[20] J. Fan and R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, Journal of the American statistical Association, 96 (2001) 1348–1360.