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