We describe the application of structured imaging with a single-pixel camera to imaging through fog. We demonstrate the use of a high-pass filter on the detected bucket signals to suppress the effects of temporal variations of fog density and enable an effective reconstruction of the image. A quantitative analysis and comparison of several high-pass filters are demonstrated for the application. Both computational ghost imaging and compressive sensing techniques were used for image reconstruction and compressive sensing was observed to give a higher reconstructed image quality.