中文摘要：

单一基函数不能对同时包含边缘和纹理信息的自然图像进行最优压缩传感图像重构.本文根据Meyer的卡通–纹理图像模型和生物视觉原理,用拉普拉斯塔式分解和圆对称轮廓波分别表示图像的光滑成分和边缘成分,并构造了窄带轮廓波变换实现纹理成分的稀疏表示.三种稀疏变换的基函数分别与视觉皮层中的侧膝体、简单细胞及栅格细胞的感受野类似.结合三种图像稀疏表示方法和凸集交替投影算法提出了基于混合基稀疏表示的压缩传感图像重构算法.实验结果表明,与基于块匹配三维变换迭代收缩的图像重构算法比较,本文算法能获得更高的图像重构质量.

英文摘要：

For a natural image which includes both edge and texture information,the single basis function cannot reconstruct the image for compressed sensing optimally.In this paper,according to the Meyer s cartoon-texture model and biological vision function,the smooth and edge components are represented by Laplacian pyramid and circular symmetric contourlet,respectively,and the narrow-band contourlet is constructed to represent texture component sparsely.The basis functions of the three sparse transforms are similar to the receptive fields of the lateral geniculate nucleus,simple cells and grating cells in primary visual cortex.On the basis of the three sparse image representations and convex alternative projection algorithm,the image reconstruction for compressed sensing based on the combined sparse representation is proposed.Compared to the image reconstruction algorithm of block matching 3D transform shrinkage,the proposed algorithm can achieve higher image reconstruction performance.