Synthetic aperture radar (SAR) despeckling is an inverse-recovery problem in which multiplicative non-Gaussian noise must be suppressed without erasing scattering structures. We revisit a nonlocal sparse estimator that applies a log--Yeo--Johnson transformation, stacks similar patches into groups, codes each group on its own left singular basis, and shrinks the resulting coefficients. Three quantities usually treated as tunable are shown to be fixed by this construction. First, the group dictionary is orthonormal, so the weighted Lasso admits an exact coefficient-wise soft-threshold solution: the iterative inner solver is unnecessary, and the two apparent weighting matrices are the numerator and denominator of a single threshold field rather than independent modules. Second, because the dictionary is estimated from the noisy group itself, its retained subspace absorbs speckle in proportion to the group aspect ratio $γ=p^2/K$; a random-matrix argument converts the corresponding regularization constant into a geometry-calibrated correction and collapses patch size, group size, and shrinkage scale into one analytically determined degree of freedom. Third, singular projection makes the coefficient noise nearly Gaussian at every tested look number, which locates the point at which an exact speckle likelihood ceases to be informative. The resulting estimator is deterministic, training-free, and applies one set of analytically determined settings to every image and sensor. It ranks first in 18 of 24 PSNR/SSIM comparisons against twelve published methods on three synthetic benchmarks, and attains the lowest mean deviation of the ratio image from the theoretical speckle model over six real-SAR configurations from five sensors. Code is available \href{https://github.com/Teriri1999/Geometry-Calibrated-Closed-Form-Shrinkage-for-SAR-Despeckling}{here}.
Multiplicative Gamma noise is a signal-dependent degradation in coherent imaging; synthetic aperture radar (SAR) despeckling is its most prominent real-world instance. Existing diffusion denoisers parameterize their forward process by abstract signal-to-noise schedules rather than by the physical look number $L$, so different deployment scenarios typically require separately trained models, and transfer from synthetic Gamma training to real SAR remains challenging without clean ground truth. We introduce $γ$-Bridge, a look-parametric bridge whose schedule $L(t)$ connects the noisy observation at $L_{obs}$ to the clean limit through exact multiplicative Gamma marginals. Its closed-form Gamma--Lévy reverse posterior admits both stochastic and deterministic processes, while observation conditioning and a two-step consistency loss stabilize multi-step inference in the low-SNR single-look regime. Because bridge time directly represents $L$, one conditioned network can smart-start from any admissible input look and stop at a target look number. These two orthogonal controls enable zero-shot restoration over the full admissible grid after training only at $L_{obs} = 1$ on natural images with synthetic Gamma corruption. Combined with a homogeneous-patch look estimator, $γ$-Bridge processes data from six spaceborne and airborne SAR sensors without sensor-specific fine-tuning, achieving leading results on standard synthetic benchmarks while providing physically interpretable input and output controls absent from prior denoisers. Codes are released \href{https://github.com/Teriri1999/GammaBridge}{here}.