中文摘要：

为减少在图像反卷积过程中的计算时间以及存储空间，提出了对基于循环边界和对称边界的图像分别采用离散傅里叶变换（DFT）和离散余弦变换（DCT）这两种快速算法替代传统卷积和反卷积的方法。从数学角度严格分析了卷积和反卷积原理，利用矩阵对角化极大地降低了算法的计算负担，避免了因模糊矩阵庞大且不易存储而造成的计算十分耗时的缺点。模拟算例结果表明，在基于循环和对称边界条件下这两种快速算法有效可行，取得了良好的图像重建效果。

英文摘要：

To reduce the computing time and the storage space during image deconvolution, two fast algorithms, separately based on the discrete fourier transform （DFT） and the discrete cosine transform （DCT）, are raised to replace the traditional method of convolution and deconvolution which are applied to process images with cyclic and Neumann boundary condition. The convolution theory is rigorously analyzed from a mathematical point of view. Computing burden is largely decreased by means of matrix diagonalization and the disadvantage of high time comsumption which is caused by the huge dimensions of blurry matrix is avoided. The simulation examples indicate that these two fast algorithm are effective and practicable in the condition of cyclic and Neumann boundary. And favorable results of image reconstruction are achieved.