关键词: 可压缩传感, 非线性恢复, 稀疏性, 块效应

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