DCT Steganography Problem
The inverse DCT is used to decompress the image, but you do not have to decompress the image.  If you decompress the image, I suppose that you also compress it again for reading the DCT coefficients, and as far as JPEG is a lossy format, some DCT coefficients could change their value. 

But JPEG does not work in this way. In JPEG the DCT coefficients are compressed and saved into the file. It is the visualization tool that decompresses the image to show it to the user.