An Efficient Model Based on Smoothed ℓ0 Norm for Sparse Signal Reconstruction

• Yangyang Li,
• Guiling Sun,
• Zhouzhou Li,
• Tianyu Geng,

Vol. 13, No. 4, April 29, 2019
10.3837/tiis.2019.04.016, Download Paper (Free):

• Compressed sensing
• smoothed ℓ0 norm
• generalized approximate function
• reconstruction algorithm

Abstract

Compressed sensing (CS) is a new theory. With regard to the sparse signal, an exact reconstruction can be obtained with sufficient CS measurements. Nevertheless, in practical applications, the transform coefficients of many signals usually have weak sparsity and suffer from a variety of noise disturbances. What's worse, most existing classical algorithms are not able to effectively solve this issue. So we proposed an efficient algorithm based on smoothed ℓ0 norm for sparse signal reconstruction. The direct ℓ0 norm problem is NP hard, but it is unrealistic to directly solve the ℓ0 norm problem for the reconstruction of the sparse signal. To select a suitable sequence of smoothed function and solve the ℓ0 norm optimization problem effectively, we come up with a generalized approximate function model as the objective function to calculate the original signal. The proposed model preserves sharper edges, which is better than any other existing norm based algorithm. As a result, following this model, extensive simulations show that the proposed algorithm is superior to the similar algorithms used for solving the same problem.

Statistics

Cite this article