Hyper-parameter tuning, and especially regularisation parameter estimation, is a challenging but essential task when solving inverse problems. The solution is obtained here through the minimization of a functional composed of a data fidelity term and a regularization term. Those terms are balanced through a (or several) regularisation parameter(s) whose estimation is made under an unrolled strategy together with the inverse problem solving. The resulting network is trained while incorporating information on the model through Maximum a Posteriori estimation which drastically decreases the amount of data needed for the training and results in better estimation results. The performances are demonstrated in a deconvolution context where the regularisation is performed in the wavelet domain.