SURE Soft-Threshold Risk
Choose denoising strength with a risk estimate that does not require knowing the true signal.
Free theory articleChoose denoising strength with a risk estimate that does not require knowing the true signal.
Concept & interpretation
Stein's Unbiased Risk Estimate (SURE) provides a way to estimate the mean squared error of a nearly arbitrary nonlinear estimator without knowing the true underlying signal. This is particularly powerful for tuning the threshold parameter in soft-thresholding denoising.
Experiment
In the Interactive Module, you can vary the underlying signal type (Sparse, Zeros, Strong), the threshold parameter λ, and the noise level σ. To reproduce the calculation:
- Set the Data control to "Sparse".
- Set Threshold to 0.5.
- Set Noise sigma to 0.5.
- Observe the computed SURE total risk estimate, which is identical to the calculated 0.63.
Observe how the SURE estimate tracks the true realized error. While the deterministic samples provided illustrate the behavior of SURE, they do not prove unbiasedness over repeated samples. Notice that SURE can sometimes be negative; it should never be artificially clamped to 0.