压缩感知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。目前的压缩感知算法大部分针对灰度图像重构,而对彩色图像的重构问题研究很少。由于彩色图像三通道之间有很高的相关性，简单地将灰度图像重构方法分别应用于彩色图像的三个通道得到的彩色图像重构质量不高。为了提高彩色图像重构质量，利用具有近似平移不变性特性的双树复数小波作为自然图像的稀疏表示，提出了基于双树复数小波局部高斯模型的彩色图像压缩感知重构算法，该算法在重构时充分利用了彩色图像通道间的互相关性和小波系数的局部邻域统计分布的先验知识。实验结果表明，重构的彩色图像具有较高的峰值信噪比（PSNR）和较好的视觉效果。

Compressed sensing system can reconstruct the original image from fewer measurements using the sparse priors of image. Current research in compressed sensing has devised algorithms for grayscale images, but there are few methods for color images. Since each of the color channels is highly correlated, the result of simply extending the reconstruction algorithm of grayscale images to three channels of color images is not satisfying. Aiming at improving the reconstruction quality of color images, compressed sensing of color images based on local Gaussian model in the dual-tree complex wavelet is proposed, which uses the dual-tree complex wavelet having the property of translation invariance as the sparse representation of natural images. Priors of the inter-cross correlation of three channels of color images and the local neighbor statistic distribution of the wavelet coefficients are applied in reconstruction. Experimental results show that the proposed algorithm can improve the peak signal-to-noise ratio and the visual quality.