一种最速下降的贪婪迭代算法

压缩传感应用于图像压缩重构的算法通常有凸优化算法和贪婪迭代算法两大类.一般而言,凸优化算法重构概率高、速度较慢,贪婪迭代算法具有较快的重构速度,但损失了重构质量.结合凸优化算法中的最速下降法及贪婪迭代算法中的正交匹配算法(OMP),提出了一种新的算法,并应用于一维信号和二维图像信号的压缩重构实验,且深入对比分析了不同降采样矩阵对新算法的影响.结果发现,对同一降采样矩阵,即使图像的纹理不同,新算法在重构质量及重构时间上都优于原始的OMP算法.

Greedy iterative algorithm of the steepest descent

When Compressed Sensing （CS） model is applied to the compression-reconstruction of the image, the solving algorithm usually can be categorized as convex optimization algorithm and greedy iterative algorithm. In general, the convex optimization algorithm has a higher reconstruction rate but a slower speed, while the greedy iterative algorithm has a faster speed with a loss of the reconstruction quality. Based on one of convex optimization algorithm, the Orthogonal Matching Algorithm （OMP）, and one of greedy iterative algorithm, the steepest descent method, a new algorithm is proposed in this paper. And the new algorithm is applied to one dimensional signal and two-dimensional image signal for compression - reconstruction experiments. The different downsampling matrix effect of this algorithm is also analyzed. Results show that for the same downsampling matrix, the new algorithm is better than the original OMP algorithm both in terms of the reconstruction quality and the reconstruction time when applied for images with different textures.