This paper describes a new method that allows "Barge-In" in various environments for robot audition. "Barge-in" means that a user begins to speak simultaneously while a robot is speaking. To achieve the function, we must deal with problems on blind dereverberation and echo cancellation at the same time. We adopt Independent Component Analysis (ICA) because it essentially provides a natural framework for these two problems. To deal with reverberation, we apply a Multiple Input/Output INverse-filtering Theorem-based model of observation to the frequency domain ICA. The main problem is its high-computational cost of ICA. We reduce the computational complexity to the linear order of reverberation time by using two techniques: 1) a separation model based on observed signal independence, and 2) enforced spatial sphering for preprocessing. The experimental results revealed that our method improved word correctness of reverberant speech by 10-20 points.