中文摘要：

提出了一种组合小波变换与曲波变换稀疏约束的图像插值算法。利用小波变换对图像纹理成份和曲波变换对图像卡通成份的稀疏表示特性,首先将图像插值问题转化成稀疏约束的图像重建问题,然后通过迭代投影对复原最优化问题进行求解,从而实现成份自适应的图像插值。实验结果表明,相比于现在有图像插值算法,本文算法可以显著地提高被插值图像的峰值信噪比（PSNR）和视觉质量。

英文摘要：

A sparsity constrainted image interpolation algorithm is presented based on wavelet and curvelet transform.The proposed algorithm exploits the wavelet transform′s sparse representation of the texture components in images and curvelet transform′s sparse representation of the cartoon components.The image interpolation is turned into the sparsity constrainted image restoration.An iterative projection process is used to drive the solution towards an improved high-resolution image.Experimental results demonstrate that our interpolation algorithm substantially improves the PSNR and the subjective quality of zoomed images over conventional methods.