The state-of-the-art algorithms of determined blind source separation (BSS) methods based on the independent component analysis
(ICA) have gained computational efficiency by the majorizationminimization (MM) principle with a price of losing flexibility. That is, replacing and comparing different source models are not easy in such MM-based framework because it requires efforts to derive a new algorithm each time when one changes the model. In this paper, a general framework for obtaining an ICA-based BSS algorithm is proposed so that a source model can easily be replaced because only a single line of the algorithm must be modified. A sparsity-based extension of the independent vector analysis and a low-rankness-based BSS model using the nuclear norm are also proposed to demonstrate the simplicity and easiness of the proposed framework.