Abstract
The \( L_{1/2} \) regularization has been considered as a more effective relaxation method to approximate the optimal \( L_{0} \) sparse solution than \( L_{1} \) in CS. To improve the recovery performance of \( L_{1/2} \) regularization, this study proposes a multiple sub-wavelet-dictionaries-based adaptive iteratively weighted \( L_{1/2} \) regularization algorithm (called MUSAI-\( L_{1/2} \)), and considering the key rule of the weighted parameter (or regularization parameter) in optimization progress, we propose the adaptive scheme for parameter \( \lambda_{d} \) to weight the regularization term which is a composition of the sub-dictionaries. Numerical experiments confirm that the proposed MUSAI-\( L_{1/2} \) can significantly improve the recovery performance than the previous works.
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References
Guo J, Song B, He Y, Yu FR, Sookhak M. A survey on compressed sensing in vehicular infotainment systems. IEEE Commun Surv Tutorials. 2017;19(4):2662–80.
Luo Y, Wan Q, Gui G, Adachi F. A matching pursuit generalized approximate message passing algorithm. IEICE Trans Fundam Electron Commun Comput Sci. 2015;E98–A(12):2723–7.
Gao Z, Dai L, Han S, Chih-Lin I, Wang Z, Hanzo L. Compressive sensing techniques for next-generation wireless communications. IEEE Wirel Commun. 2018; 2–11.
Shi Z, Zhou C, Gu Y, Goodman NA, Qu F. Source estimation using coprime array: a sparse reconstruction perspective. IEEE Sens J. 2017;17(3):755–65.
Hayashi K, Nagahara M, Tanaka T. A user’s guide to compressed sensing for communications systems. IEICE Trans Commun. 2013;E96–B(3):685–712.
Donoho DL. High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension. Discret Comput Geom. 2006;35(January):617–52.
Yilmaz O. Stable sparse approximations via nonconvex optimization. In IEEE international conference on acoustics, speech and signal processing, 2007; 2008. p. 3885–8.
Chartrand R. Nonconvex compressed sensing and error correction. In: IEEE international conference on acoustics, speech and signal processing 2007; 2007, no. 3. p. 889–92.
Chartrand R. Exact reconstruction of sparse signals via nonconvex minimization. IEEE Sig Process Lett. 2007;14(10):707–10.
Xu Z, Chang X, Xu F, Zhang H. L1/2 regularization: a thresholding representation theory and a fast solver. IEEE Trans Neural Netw Learn Syst. 2012;23(7):1013–27.
Ahmad R, Schniter P. Iteratively reweighted L1 approaches to sparse composite regularization. IEEE Trans Comput Imaging. 2015;1(4):220–35.
Acknowledgements
This research was funded by State Grid Corporation Science and Technology Project (named ‘Research on intelligent patrol and inspection technology of substation robot based on intelligent sensor active collaboration technology’).
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Peng, Q. et al. (2020). An Adaptive Iteratively Weighted Half Thresholding Algorithm for Image Compressive Sensing Reconstruction. In: Liang, Q., Liu, X., Na, Z., Wang, W., Mu, J., Zhang, B. (eds) Communications, Signal Processing, and Systems. CSPS 2018. Lecture Notes in Electrical Engineering, vol 516. Springer, Singapore. https://doi.org/10.1007/978-981-13-6504-1_22
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DOI: https://doi.org/10.1007/978-981-13-6504-1_22
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