Compressed sensing signal reconstruction involves finding the sparse solution of an underdetermined system of linear equations. This problem has three common solutions:minimizing the l-norm

l-norm

and l-norm. Minimizing the l-norm can solve this problem

but the method belongs to NP complete. Meanwhile

the l-norm has no solution in theory

and the l-norm is not a convex function. Under this background

this paper presents a recovery method of compressed sensing signals based on regularized smooth convex optimization. To obtain the global optimal solution

a convex function in the entire space is first designed as the objective function of optimization to fit the l-norm of a signal. Second

the optimization problem with variables is transformed into optimization problems with one variable. Finally

a fast iterative shrinkage-thresholding algorithm is proposed to find the solution

with the convergence speed being that of quadratic convergence. Experimental results show that the method is robust and fast compared with three other types of algorithms. Specifically

the reconstruction time of the proposed method is approximately 50% of that of the other algorithms when the signal has more than 150 dimensions. In the real data experiments

the F-norm of the reconstructed signal and the original signal difference with the proposed method is approximately 70% of the other algorithms. The proposed algorithm with a high compression ratio and a good restoration effect is well-suited for processing large data. It meets the requirements for application in information retrieval

dictionary learning

image compression

and so on.