Many source separation algorithms fail to deliver robust performance when applied to signals recorded using highdensity microphone arrays where distance between sensor elements is much smaller than the wavelength of the signal of interest. This can be attributed to limited dynamic range (determined by analog-to-digital conversion) of the sensor which is insufficient to overcome the artifacts due to cross-channel redundancy, non-homogenous mixing and high-dimensionality of the signal space. In this paper we propose a novel framework that overcomes these limitations by integrating learning algorithms directly with analog-todigital conversion. At the core of the proposed approach is a novel regularized min-max optimization approach that yields “delta-sigma” limit-cycles. An on-line adaptation modulates the limit-cycles to enhance resolution in the signal sub-spaces containing non-redundant information. Numerical experiments simulating far-field recording conditions demonstrate cons...