利用分块循环矩阵对离散图象进行重建

论文讨论了图象重建的意义,提出了离散图象采样的Nyquist准则,并将图象重建的问题变成了矩阵方程的解的问题,讨论了分块Toeplitz矩阵,分块循环矩阵和离散傅立叶变换之间的关系,并利用其关系对非均匀采样图象提出了一种重建方法,该方法可以直接利用离散傅立叶变换,不需要迭代,并且可以实时进行。在文章末尾用该方法对一离散图象进行了仿真,结果表明该算法是确实有效的。

Using Block Circulant Matrices to Reconstruct Discrete Image

In this paper,the authors discuss the significant o f image reconstruction,propose the Nyquist principle of dis-crete image sampli ng,and turn the problem of image reconstruction into solving a matrix function .The relations of block Toeplitz matrix,block circulant matrix and discrete F ourier transform are discussed.Using these relations,a direct method is presen ted to reconstruct non-uniform sampling image.This method doesn't need iterati ve and can be adapted to real-time reconstruction.In the end they do some si mulations,the result shows that this method is effective.