One photograph, both jobs — the ranking flips

scikit-image’s astronaut, averaged to 256 × 256, is cut into 8 × 8 blocks (the block size JPEG uses) and folded into a 4-way tensor 32 × 32 × 64 × 3: block row, block column, position within the block, colour.

• Compression (threshold 28 dB PSNR): CP wins. Tucker needs roughly twice CP’s storage, because the layout modes need nearly all their length.
• Prediction (half the pixels hidden): Tucker predicts the hidden pixels clearly better. With the layout modes kept whole, Tucker gives every block its own coefficients; CP ties block (I, J) to a product a_Ir · b_Jr — the tie that lets it compress is exactly what stops it predicting.
• Neither beats the mean of the observed 3 × 3 neighbours on random single-pixel holes.

CP compresses, Tucker predicts — and a symmetric core rarely bites, but when entities play both roles, it always does.