To obtain the inexpensive data compression method for a high resolution image and print image data having high image quality at high speed.

Since the difference between adjacent pixels of high resolution image data or the like is small with high probability probabilistically, after the data are smoothed and quantized for the purpose, the difference in the scanning direction 3 is taken as 4 and 5 in the figure, data are coded with an encoding method at a high compression rate that is completely reconstructable and an image within a range of error in smoothing or quantizing the original image is compressed and reconstructed at high efficiency.