Abstract
Compressed sensing theory is widely used in the field of fault signal diagnosis and image processing. Sparse recovery is one of the core concepts of this theory. In this paper, we proposed a sparse recovery algorithm using a smoothed l0 norm and a randomized coordinate descent (RCD), then applied it to sparse signal recovery and image denoising. We adopted a new strategy to express the (P0) problem approximately and put forward a sparse recovery algorithm using RCD. In the computer simulation experiments, we compared the performance of this algorithm to other typical methods. The results show that our algorithm possesses higher precision in sparse signal recovery. Moreover, it achieves higher signal to noise ratio (SNR) and faster convergence speed in image denoising.
Highlights
In recent years, compressed sensing (CS) has become an essential mathematical tool in the field of information theory [1,2]
CS theory suggests that a signal can be recovered from fewer samples than suggested by the Shannon–Nyquist sampling rate given that the original signal is sparse or approximately sparse in certain representation domains
We focus sparse recovery method directly determines the quality of signal recovery [7]
Summary
In recent years, compressed sensing (CS) has become an essential mathematical tool in the field of information theory [1,2]. The sparse representation of f is obtained by a specific mathematical transformation Ψ, as shown in Equation (2) and Figure 2. Ψ is the sparse dictionary, and s is the sparse representation coefficient, such that signal fEquation can be recovered indirectly by constructing the sparse coefficients, which is shown in (3) and Figure 3. Where Ψ is the sparse dictionary, and s is the sparse representation coefficient, such that signal f can fEquation can (3).
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