中文摘要：

压缩传感理论将信号的采样与压缩同时进行，利用信号在变换基上可以稀疏表示的先验知识，从比香农采样少得多的观测值中重构原始信号。近年来，两步迭代阈值算法作为一种求解反问题的优化方法，因其与多尺度几何分析存在紧密联系，且算法参数少，思想比较简单等特点，已经应用到了压缩重构中。但其使用时域的软硬阈值算子，不能获得很好的图像稀疏表示，从而使得算法重构精度不高。针对上述问题，在研究两步迭代阈值算法的基础上，提出一种自适应的两步迭代阈值算法。该算法利用当前估计值提供的信息自适应估计步长参数，保证了估计值向最优解方向移动，提高了算法的重构精度，且针对其稀疏表示信号能力不足的缺点，运用高斯混合尺度模型对曲波邻域系数进行建模，充分利用曲波变换平移不变性和多方向选择性的优点，增加了图像表示的稀疏度。最后将其应用到图像压缩重构中，实验结果表明，该算法在峰值信噪比和主观视觉上都优于小波域高斯混合尺度模型和曲波硬阈值重构方法。

英文摘要：

Compressed sensing theory samples and compresses the signals at the same time and uses the prior knowledge that signals can be represented sparsely in the transform domain to reconstruct the original signals with less measurements than Shannon-Nyquist theory. Recently, two-step Iterative Shrinkage/Threshold algorithm has been applied to compressed recon- struction as an optimization method to solve inverse problems for its tight connection with muhi-scale geometry analysis, fewer parameters and simplicity. Using the hard and soft threshold operators in the time domain makes it hard to obtain sparse rep- resentation for two dimensional images. Consequently, the reconstruction precision of the algorithm is low. Based on the TWIST algorithm, an adaptive two-step Iterative Shrinkage/Threshold algorithm is presented. It makes use of the information obtained from current estimated values to calculate the step parameters and ensure the estimate value moving towards the opti- mum solution to improve its reconstruction precision. Regarding the poor ability to represent images sparsely, we use the Gaussian scale mixture model to model the curvelet neighborhood coefficients and enhance the ability of image sparse repre- sentation with the shift-invariance and directional-selectivity of the curvelet transform. Finally, the method is applied to image compression reconstruction and the experimental results show that it is better than both, the wavelet Gaussian scale mixture models and the curvelet hard threshold reconstruction methods in terms of subjective visual and peak signal noise ratio.