In order to effectively improve both subjective and objective qualities of the compressed images with low bit rate, to reduce the data for image recovery and to save storage space and computational complexity, a fast compressed sensing image recovery algorithm based on multi-wave transform is proposed in this paper. The algorithm applies compressed sensing theory to the image recovery field, establishes recovery model and reconstructs signal accurately and efficiently from small amounts of linear measurements much fewer than its actual dimension using sparse priors of signal.Matlab is adopted for simulation. The experimental results show that the algorithm, compared with other typical reconstruction algorithm, can get higher PSNR and improve recovery efficiency when the observation data are similar.%为了能够有效地改善低码率压缩图像的主客观质量，减少图像复原所需观测数据量，节约存储空间和计算量，提出了一种基于多层小波变换的压缩感知图像快速复原算法。该算法将压缩感知理论中的信号重构方法运用于图像复原领域，建立基于压缩感知的图像复原模型，通过少量低维投影空间的测量值并根据信号稀疏表示的先验知识对信号进行精确或高概率的复原。通过Matlab进行实验仿真，结果表明，该算法与传统的图像复原算法相比，通过相同的观测数据量可以获得更高的PSNR，复原效率也得到了提高。
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