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