That solution is one of those things where the solution seems obvious as soon as it is mentioned. At least if you are familiar with Fourier transforms. You want

That solution is one of those things where the solution seems obvious as soon as it is mentioned. At least if you are familiar with Fourier transforms. You want to remove a periodic pattern from an image, and of course that will be easier to do in phase space than spatial space. Interestingly, filtering out high frequency components from the Fourier transform of the image is exactly how JPEG lossy compression works, so compressing the image as a jpeg would likely have a similar result.