LoTA-N2N: Local Trace Adaptation for Zero-Shot Self-Supervised Image Denoising

Many self-supervised image denoising methods minimize the mean squared error (MSE) between denoiser predictions and surrogate targets constructed from noisy observations. They justify this training under different assumptions, such as suitable noise independence and unbiasedness, weak corruption, clean-neighbor similarity, or a compatible corruption model. We revisit these training objectives and show that self-supervised MSE differs from supervised MSE by a parameter-independent constant and a trace term. From this perspective, existing assumptions eliminate or suppress the trace term, narrowing the gap between self-supervised and supervised objectives up to a constant. This helps explain why training with surrogate targets generated from noisy images can yield effective denoising. Motivated by this understanding, we propose to estimate and penalize its magnitude alongside reconstruction, reducing reliance on assumptions that suppress it implicitly. However, a small global trace can conceal large regional discrepancies through cancellation of positive and negative contributions. We therefore introduce LoTA-N2N, a two-stage zero-shot denoising framework with local trace correction. A denoiser first learns from complementary sub-images of a single noisy observation and is frozen to provide clean-image proxies. These proxies enable interaction estimates whose absolute magnitudes are penalized region by region during adaptation. We prove that this local penalty prevents cancellation between regions and yields a supervised-risk upper bound with slack controlled by teacher-estimation error. Experiments demonstrate improvements over iteration-matched MSE adaptation under independent, spatially varying, and mixed noise.