The problem of blind joint FIR-MIMO channel and data estimation is addressed in this paper. Based on a regularized DML (Deterministic Maximum Likelihood) formulation of the problem, a bilinear approach is used in order to estimate jointly the channel impulse responses and the input data. This regularization is introduced as a penalty function added to the classical DML criterion representing the a priori information about the problem in order to enhance the accuracy of the estimation. Two types of priors information are considered for the transmitted data: the finite alphabet simplicity or the sparsity. The sparsity prior was also considered for channel impulse responses. The key advantage of the proposed criteria is their convexity when optimized alternatively over the channel and the input data. The proposed approach allows to improve further the estimation accuracy of such a blind estimation problem but suffers from a relatively high computational cost. Hence, a reduced complexity implementation of the latter has been proposed at the end of the paper, in an adaptive scheme for high dimensional or streaming data situations.