Ensemble Averaging Experiment:
Output
The ensemble averaging showed no discernible patterns or periodicity in the coefficients. The matrices show the DCT frequency coefficients for the DCT's of the difference images for shifts of 0 through 8 pixels. The fact that all values are zero except for the horizontal top row of coefficients indicates that the additional artifacts that show up in the difference image (and thus the shifted, recompressed JPEG) are strictly due to the shift, and not to any other phenomenon. The shift was in the horizontal direction, and thus the horizontal frequencies are effected; hence, the top horizontal row of coefficients being different than zero.
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clear (0 shift) blockDCTave SUM8x8AVE = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 clear (1 shift) blockDCTave SUM8x8AVE = Columns 1 through 7 0 0.3141 0.7526 0.2254 0.9922 1.0367 0.2041 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Column 8 0.1716 0 0 0 0 0 0 0 clear (2 shift) blockDCTave SUM8x8AVE = Columns 1 through 7 0 0.1057 0.6647 0.3945 0.7031 0.5670 -0.0386 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Column 8 0.2219 0 0 0 0 0 0 0 clear (3 shift) blockDCTave SUM8x8AVE = Columns 1 through 7 0 0.0522 0.1057 0.8522 0.0586 0.4638 0.8779 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Column 8 -0.1749 0 0 0 0 0 0 0 clear (4 shift) blockDCTave SUM8x8AVE = Columns 1 through 7 0 0.1018 -0.0648 0.9359 1.4141 0.3657 -0.1973 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Column 8 0.0930 0 0 0 0 0 0 0 clear (5 shift) blockDCTave SUM8x8AVE = Columns 1 through 7 0 1.0554 0.5599 0.0516 0.5430 0.9480 0.6475 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Column 8 0.1564 0 0 0 0 0 0 0 clear (6 shift) blockDCTave SUM8x8AVE = Columns 1 through 7 0 0.8415 0.7563 0.9649 0.7383 0.6542 0.4478 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Column 8 0.2430 0 0 0 0 0 0 0 clear (7 shift) blockDCTave SUM8x8AVE = Columns 1 through 7 0 0.6836 0.2988 0.5751 0.4219 0.3461 0.2314 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Column 8 0.1205 0 0 0 0 0 0 0 clear (8 shift) blockDCTave SUM8x8AVE = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0