IEEE Trans Neural Netw Learn Syst. 2018 Apr;29(4):1132-1146. doi: 10.1109/TNNLS.2017.2658953. Epub 2017 Feb 15.
This paper proposes two homotopy methods for solving the compressed sensing (CS) problem, which combine the homotopy technique with the iterative hard thresholding (IHT) method. The homotopy methods overcome the difficulty of the IHT method on the choice of the regularization parameter value, by tracing solutions of the regularized problem along a homotopy path. We prove that any accumulation point of the sequences generated by the proposed homotopy methods is a feasible solution of the problem. We also show an upper bound on the sparsity level for each solution of the proposed methods. Moreover, to improve the solution quality, we modify the two methods into the corresponding heuristic algorithms. Computational experiments demonstrate effectiveness of the two heuristic algorithms, in accurately and efficiently generating sparse solutions of the CS problem, whether the observation is noisy or not.
本文提出了两种同伦方法来解决压缩感知（CS）问题，将同伦技术与迭代硬阈值（IHT）方法相结合。同伦方法通过沿同伦路径跟踪正则化问题的解，克服了 IHT 方法在正则化参数值选择上的困难。我们证明了所提出的同伦方法生成的序列的任何聚集点都是问题的可行解。我们还给出了所提方法的每个解的稀疏水平的上界。此外，为了提高解的质量，我们将这两种方法修改为相应的启发式算法。计算实验表明，这两种启发式算法在准确有效地生成 CS 问题的稀疏解方面是有效的，无论观察结果是否存在噪声。
