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In this paper, we will generate a convex iterative FP thresholding algorithmto solve the problem $(FP^{\lambda}_{a})$. Two schemes of convex iterative FPthresholding algorithms are generated. One is convex iterative FP thresholdingalgorithm-Scheme 1 and the other is convex iterative FP thresholdingalgorithm-Scheme 2. A global convergence theorem is proved for the convexiterative FP thresholding algorithm-Scheme 1. Under an adaptive rule, theconvex iterative FP thresholding algorithm-Scheme 2 will be adaptive both forthe choice of the regularized parameter $\lambda$ and parameter $a$. These arethe advantages for our two schemes of convex iterative FP thresholdingalgorithm compared with our previous proposed two schemes of iterative FPthresholding algorithm. At last, we provide a series of numerical simulationsto test the performance of the convex iterative FP thresholdingalgorithm-Scheme 2, and the simulation results show that our convex iterativeFP thresholding algorithm-Scheme 2 performs very well in recovering a sparsesignal.

Nonconvex fraction function recovery sparse signal by convex optimization algorithm