Abstract: Compressed Sensing or Compressed Sampling（CS） is a new technique for simultaneous data sampling and compression.In this paper，the block compressed sensing for natural images is studied，where image acquisition is conducted in a block-by-block manner through the same operator.While simpler and more efficient than other CS techniques，it can sufficiently capture the complicated geometric structures of natural images.The image reconstruction algorithm involves both linear operations and nonlinear operations as projection onto the convex sets and hard thresholding in the contourlet domain to reduce blocking artifacts.Several numerical experiments demonstrate that the block CS compares favorably with existing schemes at a much lower implementation cost，and simultaneously the PSNR values of these natural images constructed by the new algorithm are improved by about 3~4 dB with the same number of CS measurements，but the computing speed is nearly identical.

Key words: compressed sensing, nonlinear reconstruction, sparsity, blocking artifacts

摘要： 可压缩传感或可压缩采样（Compressed Sensing或Compressive Sampling 简称CS）是数据采样同时实现压缩的新理论、新技术。分块CS（Block Compressed Sensing）的图像重构算法采用相同的采样算子以块×块的方式获取图像，解决了现有的CS方法中可压缩采样算子所需存储较大的问题，而且算法中应用线性算子、凸集投影法和Contourlet变换域的硬阈值法进一步优化恢复图像，能更有效捕获图像的复杂结构。实验结果表明分块CS的图像重构算法较现有的其他CS方法实现代价更低，且在相同CS观测数条件下，计算速度几乎相同的同时图像质量提高了3~4 dB。

关键词: 可压缩传感, 非线性恢复, 稀疏性, 块效应