提出了一种基于四叉树和偏微分方程的灰度图像压缩方法。该方法只需传输和处理部分稀疏像素而不是整幅灰度图像。在编码端,首先采用四叉树分割图像,然后对部分像素进行编码传输。在解码端,采用基于偏微分方程的图像插值算法再生图像,有效地消除了解码图像中的方块效应。实验表明,该方法可以获得较高的压缩比和峰值信噪比,尤其是对尺寸较大且纹理细节较少的图像更是如此,并能较好地保持原始图像中灰度变化较大的细节,可以方便地去除方块效应,具有较高的实用价值。 A gray image compression method based on quadtree and partial differential equation is proposed. The method only needs to transmit and process partially sparse pixels instead of the entire grayscale image. At the encoding end, we use quadtree to divide the image first and then encode and transmit some of the pixels. At the decoding end, the image interpolation algorithm based on partial differential equations is used to regenerate the image, which effectively eliminates the square effect in the decoded image. Experiments show that this method can obtain high compression ratio and peak signal to noise ratio, especially for the larger size and less texture details of the image, and can better maintain the original image in the gray-scale changes Details, you can easily remove the box effect, with high practical value.