The JPEG compressed and decompressed image would
fail the watermark test with even the most generous
thresholds on δ. The large range in the values of δ motivates
two changes to our previous forgery detection procedure.
Let YJ be the watermarked image after JPEG
compression and decompression, and ZJ be a possibly
forged watermarked image after JPEG processing. A new
test statistic must be defined: