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中文摘要：
压缩感知理论利用图像表示的稀疏先验知识,可以从远小于奈奎斯特抽样率的抽样点中重构图像.图像的稀疏表示和稀疏性度量是影响图像重构性能的两个重要因素.为获得更好的图像稀疏表示,文中根据简单细胞感受野特性,将圆对称轮廓波的一个倍频程尺度分裂为径向带宽比为1.414的两个尺度,构造出双密度圆对称轮廓波变换（DDCSCT）.根据DDCSCT的联合分布特性,利用二元分布模型获得了压缩传感图像重构的二阶稀疏性度量.实验结果表明,利用DDCSCT和二阶稀疏准则进行图像重构比现有的图像重构算法在峰值信噪比和主观视觉效果两方面均有显著提高.
英文摘要：
Compressed sensing uses the sparse prior of image representation, it can reconstruct image from samples much less than Nyquist rate. The sparse image representation and sparseness measure are two key ingredients which have important role on image reconstruction performance. To achieve the better sparse image representation, we split one octave scale of circular symmetric contourlet transform into two scales according to the characteristic of simple cell receptive field, and yield the double density circular symmetric contourlet transform （DDCSCT）. The radial bandwidth ratio of the DDCSCT is 1. 414. According to the characteristics of the DDCSCT joint distribution, we deduce the second order sparseness measure of image reconstruction from bivariate model. The experiment results show that proposed image reconstruction algorithm which combine DDCSCT and second order sparseness measure outperforms the classical algorithms in terms of both peak signal-to-noise ratio and visual quality.
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