在图像处理领域中,压缩传感重构是稀疏表示下的最重要的病态反问题之一。压缩传感图像重构利用图像可稀疏表示的先验知识,从比奈奎斯特采样率低得多的随机投影观测值中重构原始图像。为了克服传统的压缩传感算法中收敛速度慢和未利用变换系数的邻域统计特性的缺点,提出了基于高斯混合尺度模型的压缩传感图像重构算法,证明了独立的高斯混合尺度分布作为压缩传感重构的稀疏先验知识的可行性,结合全变差调整进一步提高算法的性能。实验结果表明,该算法有效地提高了重构图像的主观视觉效果和峰值信噪比,加快了压缩传感图像重构算法的收敛速度。

Compressed sensing image reconstruction is one of the foremost ill-posed inverse problems by sparse representation in the field of image processing. Image compressed sensing using the sparse prior of image can reconstruct the original image from far fewer measurements by random projection than Nyquist samples. To overcome the lower convergence rate and not exploiting the statistic characteristics of transform coefficients in neighborhood, the reconstruction algorithm combining Gaussian scale mixtures model is proposed. The feasibility is proved for independent Gaussian scale mixtures distribution use for the sparse prior of compressed sensing reconstruction. And then algorithmic performance is improved even more by total variation. Experiments show that the proposed algorithm effectively improves the subjective visual quality and peak signal-to-noise ratio, and accelerates the convergence of reconstruction algorithm.