Joint reconstruction and bias field correction for undersampled MR imaging

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.