基于共轭梯度的脉冲噪声去噪算法
Impulse Noise Denoising Algorithm Based on Conjugate Gradient

共轭梯度法是数值计算领域的一类重要方法。本文基于Schmidt正交化方法，提出了两种改进的Hestenes-Stiefel共轭梯度法。无需线搜索条件，它们自动满足共轭梯度法的两个重要性质，即充分下降性和共轭条件。在适当的条件下，本文证明了所设计算法的全局收敛性。最后，将这两种算法应用到脉冲噪声去噪中，初步的数值试验表明了算法的有效性。
Conjugate gradient method is an important method in numerical computation. Based on Schmidt orthogonalization, two improved Hestenes-Stiefel conjugate gradient methods are proposed in this paper. Without line search conditions, they automatically satisfy two important properties of the conjugate gradient method, namely, sufficient descent and conjugate conditions. Under appropriate conditions, the global convergence of the proposed algorithm is proved. Finally, the two algorithms are applied to impulse noise denoising, and preliminary numerical experiments show the effectiveness of the algorithm.