We propose a new framework to jointly improve spatial resolution and remove fixed structural patterns for coherent fiber bundle imaging systems, based on inverting a principled forward model. The forward model maps a high-resolution representation to multiple images modeling random probe motions. We then apply a point spread function to simulate low-resolution figure bundle image capture. Our forward model also uses a smoothing prior. We compute a maximum a posteriori (MAP) estimate of the high-resolution image from one or more low-resolution images using conjugate gradient descent. Unique aspects of our approach include (1) supporting a variety of possible applicable transformations; (2) applying principled forward modeling and MAP estimation to this domain. We test our method on data synthesized from the USAF target, data captured from a transmissive USAF target, and data from lens tissue. In the case of the USAF target and 16 low-resolution captures, spatial resolution is enhanced by a factor of 2.8.