论文标题
基于牛顿 - 步骤基于稀疏信号恢复的硬阈值算法
Newton-Step-Based Hard Thresholding Algorithms for Sparse Signal Recovery
论文作者
论文摘要
稀疏的信号回收或压缩传感可以作为某些稀疏优化问题进行配合。经典优化理论表明，类似牛顿的方法通常比非线性优化问题的梯度方法具有数值优势。在本文中，我们提出了所谓的基于牛顿 - 步骤的迭代硬阈值（NSIHT）和基于牛顿 - 步骤的硬阈值Pursuit（NSHTP）算法，以稀疏信号恢复和信号近似。与传统的迭代硬阈值（IHT）和硬阈值追击（HTP）不同，拟议的算法采用了牛顿般的搜索方向，而不是最陡峭的下降方向。 对提出的算法进行了理论分析，并确定了通过这些算法确保稀疏信号恢复成功的足够条件。我们的结果显示在限制的等轴测特性下，这是在压缩感应和信号近似领域广泛使用的标准假设之一。从合成数据恢复获得的经验结果表明，所提出的算法是有效的信号恢复方法。还通过模拟研究了我们算法的数值稳定性。
Sparse signal recovery or compressed sensing can be formulated as certain sparse optimization problems. The classic optimization theory indicates that the Newton-like method often has a numerical advantage over the gradient method for nonlinear optimization problems. In this paper, we propose the so-called Newton-step-based iterative hard thresholding (NSIHT) and the Newton-step-based hard thresholding pursuit (NSHTP) algorithms for sparse signal recovery and signal approximation. Different from the traditional iterative hard thresholding (IHT) and hard thresholding pursuit (HTP), the proposed algorithms adopts the Newton-like search direction instead of the steepest descent direction. A theoretical analysis for the proposed algorithms is carried out, and some sufficient conditions for the guaranteed success of sparse signal recovery via these algorithms are established. Our results are shown under the restricted isometry property which is one of the standard assumptions widely used in the field of compressed sensing and signal approximation. The empirical results obtained from synthetic data recovery indicate that the proposed algorithms are efficient signal recovery methods. The numerical stability of our algorithms in terms of the residual reduction is also investigated through simulations.
