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When imaging in scattering media, visibility degrades as objects become more distant. Visibility can be significantly restored by computer vision methods that account for physical processes occurring during image formation. Nevertheless, such recovery is prone to noise amplification in pixels corresponding to distant objects, where the medium transmittance is low. We present an adaptive filtering approach that counters the above problems: While significantly improving visibility relative to raw images, it inhibits noise amplification. Essentially, the recovery formulation is regularized, where the regularization adapts to the spatially varying medium transmittance. Thus, this regularization does not blur close objects. We demonstrate the approach in atmospheric and underwater experiments, based on an automatic method for determining the medium transmittance.