基于各向异性图像多尺度几何变换的压缩感知去噪算法

Denoising algorithm for compressed sensing based on anisotropic multiscale geometric transformation

从压缩感知的稀疏表示出发,借鉴离散剪切滤波器设计的原理,构造了一种新型的紧框架下的各向异性的图像多尺度几何变换对图像作最优的稀疏表示;采用具有局部随机特性的结构化随机矩阵作为观测矩阵抽样原始图像,结合前述稀疏表示,并在重构过程中采用改进的分割增广拉格朗日收缩阈值法作为重构算法。仿真实验结果表明所建立的压缩感知图像去噪重构算法能够从少量受噪声污染的观测值中重构出原始图像,且在有效消除噪声的同时更多地保留了图像的边缘和细节。

Starting from CS sparse representation,and drawing on the principles of discrete shearlet filter design,a new tight framework wavelet-based shearlet transform is constructed on anisotropic multi-scale image for optimal sparse representation. Using the random nature of having a local structured as a random matrix observation matrix sample the original image, combined with the aforementioned sparse representation,and the improved split augmented Lagrangian shrinkage threshold algorithm in the reconstruction process as the reconstruction algorithm. Simulation results show that CS denoising reconstruction algorithm can be reconstructed from the established observation that small amounts of data from noisy images,and at the same time effectively eliminate noise retain more image edges and details.