Speaker
Description
Noisier2Inverse is a self-supervised framework for solving linear inverse problems without ground-truth data. Given noisy measurements Y = AX + N with forward map A : R^n -> R^m, a reconstruction network of the form B : R^m -> R^n is trained by minimizing the surrogate risk E||AB(Y+M)-(Y-M)||^2, and B(Y+M) or B(Y) is used for inference. The theoretical foundation is a surrogate risk equivalence showing that this loss has the same minimizer as the supervised risk E||AB(Y+M) - AX||^2, provided that the added noise M is identically distributed to the noise N. In practice, however, this requirement may be difficult to satisfy or suboptimal. In this work, we generalize the Noisier2Inverse theorem to flexible noise models. For scaled noise M = cN we derive the correct surrogate target explicitly, and under a Gaussian assumption we show that for general independent M and N the optimal surrogate target takes the form Y - (sigma_N^2 / sigma_M^2) M. These results provide a principled basis for choosing the added noise in self-supervised training. As a concrete application, we consider angular deblurring in photoacoustic tomography with finite-size detectors in circular scanning geometry, where the finite detector aperture induces a convolution in the polar domain that is addressed in a self-supervised manner using the generalized framework.