We present a new method for blind document bleed through removal based on separate Markov Random Field (MRF) regularization for the recto and for the verso side, where separate priors are derived from the full graph. The segmentation algorithm is based on Bayesian Maximum a Posteriori (MAP) estimation. The advantages of this separate approach are the adaptation of the prior to the contents creation process (e.g. superimposing two hand written pages), and the improvement of the estimation of the recto pixels through an estimation of the verso pixels covered by recto pixels; Moreover, the formulation as a binary labeling problem with two hidden labels per pixels naturally leads to an efficient optimization method based on the minimum cut/maximum flow in a graph. The proposed method is evaluated on scanned document images from the 18$^{th}$ century, showing an improvement of character recognition results compared to other restoration methods.