基于混合梯度的硬阈值追踪算法

针对压缩感知（CS）中迭代硬阈值类算法迭代次数多、重构时间长的问题，提出了一种基于混合梯度的硬阈值追踪（HGHTP）算法。首先，在每次迭代中计算当前迭代点处的梯度和共轭梯度，将梯度域与共轭梯度域下的支撑集混合取并集作为下一次迭代的候选支撑集，充分利用共轭梯度在支撑集选择策略中的有用信息，优化支撑集选择策略；然后，采用最小二乘法对候选支撑集进行二次筛选，快速精确地定位正确的支撑并更新稀疏系数。一维随机信号重构实验结果表明，HGHTP算法相较于同类迭代硬阈值算法，在保证重构成功率的前提下，需要的迭代次数更少。二维图像重构实验结果表明，HGHTP算法的重构精度和抗噪性能优于同类迭代阈值类算法，在保证重构精度的情况下，HGHTP算法的重构时间相比同类算法减少了32%以上。

Hybrid gradient based hard thresholding pursuit algorithm

Aiming at the problem of large number of iterations and long reconstruction time of iterative hard thresholding algorithms in Compressed Sensing (CS), a Hybrid Gradient based Hard Thresholding Pursuit (HGHTP) algorithm was proposed. Firstly, the gradient and conjugate gradient at the current iteration node were calculated in each iteration, and the support sets in the gradient domain and conjugate gradient domain were mixed and the union of these two was taken as the candidate support set for the next iteration, so that the useful information of the conjugate gradient was fully utilized in the support set selection strategy, and the support set selection strategy was optimized. Secondly, the least square method was used to perform secondary screening on the candidate support sets to quickly and accurately locate the correct support and update the sparse coefficients. The experimental results of one-dimensional random signal reconstruction show that HGHTP algorithm needs fewer iterations than the similar iterative hard thresholding algorithms on the premise of guaranteeing the success rate of reconstruction. The two-dimensional image reconstruction experimental results show that the reconstruction accuracy and anti-noise performance of HGHTP algorithm are better than those of similar iterative thresholding algorithms, and under the condition of ensuring reconstruction accuracy, HGHTP algorithm has the reconstruction time reduced by more than 32% compared with similar algorithms.