Several phenomena have been recently exploited to circumvent scattering and have succeeded in imaging or focusing light through turbid layers. However, the requirement for the turbid medium to be steady during the imaging process remains a fundamental limitation of these methods. Here we introduce an optical imaging modality that overcomes this challenge by taking advantage of the so-called shower-curtain effect, adapted to the spatial-frequency domain via speckle correlography. We present high resolution imaging of objects hidden behind millimeter-thick tissue or dense lens cataracts. We demonstrate our imaging technique to be insensitive to rapid medium movements (> 5 m/s) beyond any biologically-relevant motion. Furthermore, we show this method can be extended to several contrast mechanisms and imaging configurations.