When an image is highly compressed by using the current coding standards, the decompressed image has noticeable image degradations such as blocking artifacts near the block boundaries, corner outliers at cross points of blocks and ringing noise near image edges. These image degradations are caused by quantization process of the 8×8 DCT coefficients. In order to restore the decompressed image, a loop-filtering algorithm and a post-filtering algorithm have been developed. The developed methods perform an adaptive filtering on the decompressed image according to blocking and ringing flags that are defined to reduce computation complexity. Performances of both algorithms are compared with respect to the image quality and the computation complexity. The comparison results show that the post-filtering is slightly better than or similar to the loop filtering with respect to peak signal-to-noise ratio (PSNR), whereas the subjective image qualities of both methods are quite similar. However, the computation complexity of the loop filtering is much less than that of the post-filtering.