  Undersampling the k-space in MRI allows saving precious acquisition time, yet
results in an ill-posed inversion problem. Recently, many deep learning
techniques have been developed, addressing this issue of recovering the fully
sampled MR image from the undersampled data. However, these learning based
schemes are susceptible to differences between the training data and the image
to be reconstructed at test time. One such difference can be attributed to the
bias field present in MR images, caused by field inhomogeneities and coil
sensitivities. In this work, we address the sensitivity of the reconstruction
problem to the bias field and propose to model it explicitly in the
reconstruction, in order to decrease this sensitivity. To this end, we use an
unsupervised learning based reconstruction algorithm as our basis and combine
it with a N4-based bias field estimation method, in a joint optimization
scheme. We use the HCP dataset as well as in-house measured images for the
evaluations. We show that the proposed method improves the reconstruction
quality, both visually and in terms of RMSE.
