In this contribution, the problem of broadband acoustic signal extraction is treated as a specific source separation problem, where the desired signal components are to be separated from all remaining undesired components. For this, we exploit the generic TRIple-N Independent component analysis for CONvolutive mixtures (TRINICON) framework. The TRINICON optimization criterion is complemented with linear constraints leading to the Linearly Constrained Minimum Mutual Information (LCMMI) criterion for desired signal extraction. A general linearly constrained update rule for iterative filter optimization is derived, which can efficiently be realized in a novel Minimum Mutual Information (MMI)-Generalized Sidelobe Canceler (GSC). The general treatment of the signal extraction problem using an MMI criterion provides several advantages: Firstly, new insights into the signal extraction problem can be derived by establishing links to both the original GSC and the Multichannel Wiener Filter (MWF). Secondly, by exploiting fundamental properties characteristic for speech and audio signals, complicated and often unreliable Voice Activity Detection (VAD)-based control mechanisms become unnecessary. Thirdly, the overall realization requires only prior information of the desired source position. An evaluation of the MMI-GSC for the double-talk situation with two concurrently active speech sources under reverberant and noisy conditions demonstrates the effectiveness of this novel approach.