Transformer-based models achieve strong performance on blind compressed image restoration (CIR) under unknown compression settings, but their densely stacked projection operators make deployment costly. We study training-free acceleration for such models through an empirical, operator-level analysis. Specifically, we profile where computation is concentrated, characterize channel-wise activation distributions under compressed inputs, and examine the singular-value decay of representative projection weights. These measurements identify the recurring projections in the attention, feed-forward, convolutional, and prompt-conditioning pathways as effective low-rank replacement targets that preserve the original inference graph. They further establish truncated SVD (TSVD) as a principled training-free baseline for blind CIR and reveal why a uniform low-rank objective is mismatched to the channel-imbalanced feature distributions of compressed images. Accordingly, we formulate Activation-Calibrated Singular Value Decomposition (ASVD) for this restoration setting, deriving low-rank factors entirely offline from pretrained weights and lightweight activation statistics gathered from only a few compressed calibration images. By weighting the decomposition with channel-wise activation magnitudes, our ASVD assigns larger penalties to errors on more active channels, requiring neither retraining nor online calibration and leaving the restoration pipeline intact. When instantiated on PromptCIR at rank 64, ASVD consistently improves PSNR-B over TSVD across four standard benchmarks under identical parameter and MAC budgets. At this operating point, the factorized model cuts parameters by 59% (34.75M to 14.34M) and computation by 16.1% (258.79 to 217.16 GMACs for a 256 x 256 input), enabling acceleration without retraining.

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