基于分数阶微积分的图像超分辨率重建

摘要

In order to solve the blurred image super-resolution reconstruction problem,the fractional calculus is combined with projection onto convex sets (POCS) to reconstruct super-resolution images.Using a fractional calculus operator to get the reference frame,through scale invariant feature transform (SIFT) matching,along with the fractional point spread function,and the imaging blurred images problem is solved by POCS,and the super-resolution reconstruction is implemented for noised or blurred images.Comparing with other superresolution algorithms,experiments show that POCS with FC-optimized SIFT has good results in several objective evaluation indeces.Especially,when the origin low-resolution image is blurred,the algorithms based on contour stencils or sparse representation will increase the degree of blurring of the image,and the image obtained has obvious improvement in clarity and better reconstruction effect.%为了解决模糊图像超分辨率重建的问题,将分数阶微积分和凸集投影相结合,实现图像的超分辨率重建.利用分数阶微分卷积获取原始参考帧,通过尺度不变特征变换(scale invariant feature transform,SIFT)配准,采用基于分数阶积分的点扩散函数,运用凸集投影,有效解决超分辨率算法对于模糊图像效果不好的问题,实现了对模糊图像的重建.实验表明,与常见的算法相比,基于分数阶微积分的凸集投影超分辨率重建算法在图像视觉效果和客观指标上均有较好的结果.特别是在图像模糊的情况下,基于稀疏表示的或轮廓模板的算法会增加图像的模糊程度,而所提算法在主观清晰度方面有明显的提高.