Directionally Weighted Total Variation for Inverse Problems

What the math gives to ML

The paper turns forward-operator sensitivity into a spatially varying total-variation metric, compensating for regions where a measurement operator is intrinsically insensitive. This is directly transferable to neural inverse solvers: instead of applying an identical TV penalty to every reconstructed pixel, weight each local image gradient by the norm of the forward model's Jacobian response at that location. The strongest implementation is a plug-in loss for an unrolled or feed-forward reconstruction network, with weights estimated from Jacobian-vector products or finite differences and detached from backpropagation. The expected benefit is reduced localization and size bias when the forward operator has a large null space or strongly nonuniform sensitivity.