  Inverse imaging problems (IIPs) arise in various applications, with the main
objective of reconstructing an image from its compressed measurements. This
problem is often ill-posed for being under-determined with multiple
interchangeably consistent solutions. The best solution inherently depends on
prior knowledge or assumptions, such as the sparsity of the image. Furthermore,
the reconstruction process for most IIPs relies significantly on the imaging
(i.e. forward model) parameters, which might not be fully known, or the
measurement device may undergo calibration drifts. These uncertainties in the
forward model create substantial challenges, where inaccurate reconstructions
usually happen when the postulated parameters of the forward model do not fully
match the actual ones. In this work, we devoted to tackling accurate
reconstruction under the context of a set of possible forward model parameters
that exist. Here, we propose a novel Moment-Aggregation (MA) framework that is
compatible with the popular IIP solution by using a neural network prior.
Specifically, our method can reconstruct the signal by considering all
candidate parameters of the forward model simultaneously during the update of
the neural network. We theoretically demonstrate the convergence of the MA
framework, which has a similar complexity with reconstruction under the known
forward model parameters. Proof-of-concept experiments demonstrate that the
proposed MA achieves performance comparable to the forward model with the known
precise parameter in reconstruction across both compressive sensing and phase
retrieval applications, with a PSNR gap of 0.17 to 1.94 over various datasets,
including MNIST, X-ray, Glas, and MoNuseg. This highlights our method's
significant potential in reconstruction under an uncertain forward model.
