Inverse problems, reconstruct the signal from the measurement

par Antoine Crosnier (ENS Lyon)

jeudi 8 janv. 2026, 10:30 → 12:30 Europe/Paris

In inverse problems, the goal is to recover an unknown signal
x from noisy measurements y=Ax+n. To address this, a reconstruction or
denoising function f can be designed such that f(y) provides an
approximation of x. In a supervised setting, this function f can be
implemented as a neural network trained on pairs of examples (x,y),
where the network learns to map y to x through f(y)=x. However,
obtaining ground-truth signals x, or even multiple noisy observations y
of the same signal, is usually difficult or impossible.
To overcome this limitation, several self-supervised approaches, such as
Equivariant Imaging and SURE, have been proposed. These methods rely
only on noisy measurements y, the measurement operator A, and knowledge
of the noise characteristics n to train f without requiring a signal x.
In practical scenarios, the noise characteristics or even the
measurement operator may be partially or completely unknown. To address
the case where the noise level is unknown but the measurement operator
and the noise model are known, the UNSURE method was developed. Despite
these advances, no self-supervised approach has yet been proposed for
situations where the measurement operator A itself is unknown. In this
work, we explored a modification of the Equivariant Imaging method to
handle this case of an unknown measurement operator.