Accurate channel modeling and estimation of active reconfigurable intelligent surface (RIS)-assisted links with densely integrated elements are essential to fully unleashing this technology's potential. This work adopts a physically consistent model incorporating mutual coupling (MC) effects, modeled via scattering parameters, in RIS-aided communication. We formulate the MC-aware channel estimation as a compressed sensing (CS) problem. The MC effect leads to an increase in the sensing matrix dimensions. This increased dimensionality substantially elevates the complexity of the formulated CS problem. To overcome this, we propose a low-complexity estimator that leverages the structure of the scattering matrix and MC mechanisms to obtain a reduced-size design sensing matrix. Numerical results demonstrate that our approach outperforms MC-unaware estimators by several dBs, achieving accuracy comparable to fully MC-aware solutions but with significantly lower complexity.

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