The compressed sensing theory is a novel data acquisition, coding and decoding theory under the condition that signal is sparse or compressible. The two-dimension wavelet decomposition, reconstruction algorithm and compressed sensing theory are introduced. It is pointed out that the theory of compressed sensing based on wavelet transform has the advantages of low computational complexity, simple structure and easy to realize in the processof image restoration. The experiment result means that the algorithm compared with other typical restoration algorithm, when the processing outputs are similar, takes up less observation data,storage space and calculation quantity. It can effectively improve both subjective and objective qualifies of the compressed images with low bit rate, and achieve better performance than other traditional algorithms.%压缩感知理论是在已知信号具有稀疏性或可压缩性的条件下,对其进行数据采集、编码和解码的新型理论.通过对二维小波分解与重构算法以及压缩感知理论的介绍,指出基于小波变换压缩感知理论在图像复原中具有计算复杂度低、结构简单和易于实现的优点.实验结果说明了该算法与一般的图像复原算法相比,相近效果下所需要的观测数据量、存储空间和计算量更少；能够有效地改善低码率压缩图像的主客观质量,改善程度也优于传统算法.
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