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Abstract: In this paper, we present an adaptive two-step contourlet-wavelet iterative shrinkage/thresholding (TcwIST) algorithm for remote sensing image restoration. This algorithm can be used to deal with various linear inverse problems (LIPs), including image deconvolution and reconstruction. This algorithm is a new version of the famous two-step iterative shrinkage/thresholding (TwIST) algorithm. First, we use the split Bregman Rudin-Osher-Fatemi (ROF) model, based on a sparse dictionary, to decompose the image into cartoon and texture parts, which are represented by wavelet and contourlet, respectively. Second, we use an adaptive method to estimate the regularization parameter and the shrinkage threshold. Finally, we use a linear search method to find a step length and a fast method to accelerate convergence. Results show that our method can achieve a signal-to-noise ratio improvement (ISNR) for image restoration and high convergence speed.

自适应轮廓波–小波迭代收缩遥感图像复原算法

研究目的：针对遥感图像的特点，使用分解模型，提高复原质量；使用自适应方法和线性搜索方法提高复原图像质量和迭代算法的收敛速度。
创新要点：使用基于稀疏字典的分解模型，提高了复原图像的质量；使用自适应方法和经验方法，弥补了复原问题先验知识不足的缺点；使用线性搜索和快速迭代算法，有效提高了算法的收敛速度。
方法提亮：首先，利用基于稀疏字典的分裂BregmanRudin-Osher-Fatemi模型，将图像分解为卡通和纹理两部分，分别用小波变换和轮廓波变换表示。接着，运用自适应方法估计正则化参数和经验方法计算收缩阈值。最后，使用线性搜索方法寻找步长，并结合快速收缩算法加速算法收敛。
重要结论：相比于两步迭代算法，基于自适应的轮廓波–小波迭代收缩算法能有效提高复原图像的改善信噪比，同时加快了算法的收敛速度。
图像复原；自适应；卡通–纹理分解；线性搜索；迭代收缩

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