中文摘要：

借助矩形NAM图像表示方法和偏微分方程技术,提出一种新的灰度图像压缩方法.该方法在编码端把原始图像逆布局为若干矩形子块,并采用坐标压缩方法存储每个子块的位置、大小.在解码端,采用偏微分方程进行图像修复,有效消除解码图像中的方块效应.该方法的时间复杂度为,其中n为灰度图像像素数.实验表明：在保持图像质量的前提下,该方法具有更高的压缩比和更少的块数,具有较高实用价值.

英文摘要：

Based on Rectangle NAM and PDE,a new compression method for gray image is proposed.On the encoder,the original image is segmented into a number of rectangular sub-block,and the method of coordinate compression is used for storaging location and size of sub-block.On the decoder,a PDE method is applied to reconstruct the image,which is effective to reduce block-effect.The time complexity is,n is the number of Gray-scale image pixels.Experiments show that the proposed approach can reduce the number of rectangular sub-block and has a higher compression ratio on the premise of remaining the image quality,which has a potential in application.