Unbiased Injection of Signal-Dependent Noise in Variance-Stabilized Range

The design, optimization, and validation of many image processing or image-based analysis systems often requires testing of the system performance over a dataset of images corrupted by noise at different signal-to-noise ratio regimes. A noise-free ground-truth image may not be available, and different SNRs are simulated by injecting extra noise into an already noisy image. However, noise in real-world systems is typically signal-dependent, with variance determined by the noise-free image. Thus, also the noise to be injected shall depend on the unknown ground-truth image. To circumvent this issue, we consider the additive injection of noise in variance-stabilized range, where no previous knowledge of the ground-truth signal is necessary. Specifically, we design a special noise-injection operator that prevents the errors on expectation and variance that would otherwise arise when standard variance-stabilizing transformations are used for this task. Thus, the proposed operator is suitable for accurately injecting signal-dependent noise even to images acquired at very low counts.