1. A method of estimating a quantization table, which was used in compression and encoding of an image block for post process filtering video output from a video decoder, the method comprising: receiving a decoded image block from the output of the video decoder, performing, by a processor, a first quantization on the image block using respective candidate quantization tables to obtain a first-quantized image block, and obtaining a first energy cost of the first-quantized image block corresponding to the respective candidate quantization tables; edge-related filtering, by the processor, the compressed image block and performing a second quantization on the filtered compressed image block using the respective candidate quantization tables to obtain a second-quantized image block, and obtaining a second energy cost of the second-quantized image block corresponding to the respective candidate quantization tables; estimating, by the processor, one of the candidate quantization tables based on the first energy costs and the second energy costs obtained by the candidate quantization tables as the quantization table that was used in compression and encoding of the image block at a video encoder; and post process filtering the decoder image block using the estimated candidate quantization table.