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Electrical impedance tomography (EIT) is used to measure regional changes in the impedance of the lung tissue caused by changes in either ventilation or perfusion. The separation of these two effects is a longstanding problem with important implications in mechanical ventilation. Unfortunately, previous approaches to perfusion/ventilation separation are not satisfactory. In this work, we introduce a new algorithmic approach, which models both signal components as non-stationary spatio-temporal Gaussian processes (GPs) and we show that the corresponding inference problem can be solved efficiently by exploiting structure in the GP’s kernel matrix. More specifically, we enable fast matrix-vector multiplications with the full kernel matrix in a novel variant of a previously proposed scalable GP approach called structured kernel interpolation. We show preliminary results of our method on a first EIT dataset.