基于两步迭代收缩法和复数小波的压缩传感图像重构

Compressed sensing image reconstruction based on two-step iterative shrinkage and complex wavelet

压缩传感系统利用图像稀疏表示的先验知识,能从少量的观测值中重构原始图像。目前压缩传感系统通常利用只有三个方向的正交小波基表示图像,应用迭代收缩法求解对应的优化问题。该方法的缺点是收敛速度慢,并且重构图像有明显的伪吉布斯效应。针对这一缺点,本文提出了结合双树复数小波稀疏图像表示和两步迭代收缩的图像重构算法,在迭代时利用前两个估计值更新当前值。实验结果表明,本文算法的重构图像视觉效果好,收敛速度比传统的重构算法快。

Compressed sensing system can reconstruct original image from fewer measurements using sparse priors of the image. In current compressed sensing literature, people always use orthogonal wavelet with three directions to represent the image, and use iterative shrinkage to solve the optimization problem. However, traditional reconstruction algorithm suffers from lower convergence rate and pseudo-Gibbs effect in the reconstructed image. Aiming at this problem, this paper presents an image reconstruction algorithm based on sparse representation of the image in dualtree complex wavelet transform domain and two-step iterative shrinkage, which uses two previous estimations to obtain a new one. The results of experiments show that the reconstructed image has better vision quality and the convergence rate is faster than that of conventional reconstruction algorithm.