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So for MRI imaging, if an image is taken, and portions of the Fourier transform image are removed so that some portion of the higher frequencies are not included, would this reduce the SNR? I assume that it would because you'd be removing a portion of the signal data. Sorry if I'm off on this but this is what intuitively seems to make sense when thinking about it.

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  • $\begingroup$ Filters will almost always remove a portion of the signal data. The question is how much signal is lost compared to how much noise is removed. If you lose 1% of your signal but remove 99% of the noise, then the ratio will increase dramatically. Indeed, so long as you remove more noise than signal, the ratio will always benefit. I don't know anything about MRIs though, so no idea what would be expected from a hi-fi filter in that environment, which is why I'm not posting this as an answer. $\endgroup$ – Wasabi Apr 21 at 16:03

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