一类信号恢复问题的投影迭代硬阈值算法

本文给出了基于L₀模求解该问题的非凸模型,借助于稀疏正则化方法来克服问题的不适定性。该模型利用紧小波框架对信号进行稀疏逼近,并利用L₀模度量稀疏性。提出了求解该模型的投影迭代硬阈值算法,并证明了算法的全局收敛性。该算法每一步都有闭式解,计算过程简洁高效。数值实验表明,方法在重建信号的视觉质量和量化指标方面均优于所对比的pFISTA方法。

A Projected Iterative Hard-Thresholding Algorithm for Signal Recovery

There is an important application background such as compressive sensing and magnetic resonance imaging to recovery the signal from partial imcomplete Fourier transform data.In this paper,a nonconvex model based on the L₀ norm is proposed to solve this problem,in which the sparse regularization is used to overcome the ill-posedness of the problem.Our model uses the tight framelet to sparsely approximate the signal and uses the L₀ norm to measure the sparsity.In this paper,a projected iterative hard-thresholding algorithm is proposed to solve the model,and the global convergence of the algorithm is proved.The proposed algorithm is efficient because each subproblem has the closed-form solution.Numerical experiments demonstrate that the proposed method is superior to the existing pFISTA method in terms of the visual quality and quantization index of the reconstructed signal.