The problem of rolling element bearing diagnosis can be viewed as that of extracting transient signals from strong additive noise. In order to separate these two kinds of signals, the problem is formulated as the minimization of an objective function which consists of two terms, a data fitting term, and a regularization term. The data fitting term reflects the conservation of energy and the regularization term reflects the prior information (initial supposition) on the objective signals to be separated. Since the objective is to separate two kinds of signals, a combined regularization scheme (distinct priori information for each signal with a target for separation) is naturally investigated. In this paper, two kinds of strategies are considered: the first one is a combination of two sparse regularization terms, and the second one is a combination of a low rank regularization term and a sparse regularization term.