Abstract—This paper investigates the problem of image reconstruction of compressed sensing. First, an improved smoothed l₀ norm (ISL0) algorithm is proposed by using modified Newton method to improve the convergence speed and accuracy of classical smoothed l₀ norm (SL0) algorithm, and to increase calculation speed and efficiency. The choice of algorithm parameter is discussed and the algorithm convergence is proven. Then, the proposed ISL0 algorithm is applied to reconstruct images of compressed sensing. We preserve low-pass wavelet coefficients after single layer wavelet transform, only measure the high-pass wavelet coefficients. Then, ISL0 algorithm is utilized to recover high-pass wavelet coefficients, and inverse wavelet transform is performed to obtain the original image. Finally, simulation results are given to demonstrate the effectiveness of the proposed algorithm. It is shown that, compared with classical SL0, SP and OMP algorithms, the proposed ISL0 algorithm performs better not only in reconstruction quality, but also in calculation complexity and noise robustness.
 
Index Terms—Compressed sensing, image reconstruction, smoothed  norm algorithm, single layer wavelet transform , modified Newton method.

Cite: Hui Zhao, Jing Liu, Ruyan Wang, and Hong Zhang, "Image Reconstruction of Compressed Sensing Based on Improved Smoothed l₀ Norm Algorithm," Journal of Communications, vol. 10, no. 5, pp. 352-359, 2015. Doi: 10.12720/jcm.10.5.352-359