中文摘要：

针对图像修复和插值等图像处理问题进行研究,通过将图像修复和插值模型在压缩感知（CS）理论的框架下进行转换,建立了新的图像修复和插值模型,该模型与CS理论中的重构模型相对应。对此转化得到的重构问题,基于图像在复数小波变换上的稀疏性,利用迭代硬阈值方法求解重构模型,进而获得重构图像。仿真和实测数据处理结果验证本文方法的有效性。

英文摘要：

This paper studies the problem of image inpainting and image interpolation.By transforming the inpainting and interpolation model under the scheme of compressed sensing,we establish a new model of inpainting and interpolation,which is corresponding to the reconstruction model in compressed sensing.To solve this new reconstruction model,this paper gives an iterated hard threshold method based on the sparsity of images decomposed on the complex wavelet.Simulated and real image results demonstrate the effectiveness of the proposed method.