Solving Inverse Problems with a Flow-based Noise Model
This work addresses image reconstruction challenges in scenarios with complex noise and non-linearities, offering a flexible approach for applications like medical imaging or signal processing, though it appears incremental as it builds on existing flow-based priors.
The paper tackles image inverse problems by using a normalizing flow prior to compute maximum a posteriori estimates, enabling handling of arbitrary noise dependencies and non-linear forward operators, with empirical validation on tasks like compressed sensing with quantized measurements and denoising with structured noise.
We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with arbitrary dependencies as well as non-linear forward operators. We empirically validate the efficacy of our method on various inverse problems, including compressed sensing with quantized measurements and denoising with highly structured noise patterns. We also present initial theoretical recovery guarantees for solving inverse problems with a flow prior.