what about if you run a 2-D FFT rather than 2-D FFT, if your hand drawing map in on a 2-D paper?
> On Apr 28, 2023, at 10:48 AM, James Holton <[email protected]> wrote: > > Its still April, but this one isn't a joke. > > The smiley-face electron density in the left panel of the attached image has > the remarkable property that any attempt to sharpen or blur the map turns it > into the frowny-face on the right. If you'd like to try this yourself, the > hidden_frown.map file is available in this tarball: > https://bl831.als.lbl.gov/~jamesh/bugreports/fft_042423.tgz > > In fact, any use of an FFT, even with the sharpening B set to zero, turns the > smiley into a frowny face. There is no way to get the smiley face back > (except opening the file again). Yes, that's right, even just a simple > back-and-forth FFT: turning this hidden_frown.map into structure factors and > then back into a map again, gives you a frowny face. This happens using > coot, ccp4 and phenix. > > Wait, what!? Isn't a Fourier transform supposed to preserve information? As > in: you can jump back and forth between real and reciprocal space with > impunity? Without introducing error? Well, yes, it is SUPPOSED to work like > that, but the 3D FFT algorithms of structural biology have a ... quirk. If > you start with structure factors and make a map out of them, you can convert > it back-and-forth as often as you want with 100% preservation of information. > However, if you start with a real-space map (such as from cryoEM), a > back-and-forth conversion gives you a different map. This new map can then be > transformed back-and-forth all you want and be 100% preserved. It has been > "christened" by the FFT, but it is not the same as the starting map, which is > impossible to recover from the FFT-transformed data. Information has been > lost. It is fine for crystallography (which starts with structure factors), > but for techniques such as cryoEM that start with maps, using an FFT changes > the data. > > What information is being lost? Sharp edges. These turn into ripples > covering all of real and reciprocal space. Do real-world data have sharp > edges? Well, the all-or-nothing masks we use to model bulk solvent are one > example. Also, if you "mask off" otherwise smooth density with an > all-or-nothing mask, you will get similar ripples. Another example of a > sharp edge might be the large changes between adjacent pixels you see when a > single electron hits a detector. For example, if you make a map with just one > non-zero voxel and run it back-and-forth through FFT you will find that voxel > loses from 50% to 99% of its value (depending on the size of the map). How > much does this actually impact cryo-EM data? That is my question. > > What evil magic did I wield to make this map? Well, I drew a smiley and > frowny face by hand, converted them to maps, and then I generated random > noise within the boundaries of the smiley face. I ran this noisy map > back-and-forth through FFT, and then subtracted the map that survives the FFT > from the pre-FFT map. This cheshire_smile.map has the interesting property > that all of the structure factors calculated from it are zero. It has an RMSD > of 1.4, but after a back-and-forth FFT this RMSD drops to 1e-7. I generated > the hidden_frown.map by simply summing the frowny.map with cheshire_smile.map. > > But isn't this map getting less noisy? Yes it is, but the interpretation > clearly changes as well. > > Why does this happen? It is because of a finite resolution cutoff. Oh! What > a relief! You don't have super-high resolution, do you? Well, no, almost > nobody has signal out beyond 1.0 A, but we do have noise. In diffraction > data this noise is removed by simply not measuring it. For map data, > however, the problem is that noise at very high frequencies (small-number > resolutions) is hard to avoid. This is because of another phenomenon NMR > spectroscopists are very familiar with: aliasing, or "folding". If any > high-spatial frequency noise exists above half the sampling rate (or "Nyquist > frequency") it still gets recorded, but shows up in a lower-frequency Fourier > coefficient. It is not possible to remove such aliasing noise after > digitization. Upon discretization of the signal (FFT or no) all these high > frequencies join with lower frequency terms, and so survive any low-pass > filtering. Darn. > > Why am I bringing this up? Because if there is noise out beyond the FFT > resolution limit it implies there is also noise out beyond the > Nyquist-Shannon limit as well. If that is the case, direct-space imaging data > may be a lot noisier than it needs to be. In general, in digital signal > processing of things like sound an analog low-pass filter is always installed > at the input of any digitizer. Perhaps this is why de-focusing works better > than being at focus? > > What is the solution? Well, for things like the bulk solvent mask I'd say > some real-space "feathering" is called for before performing FFTs. Same goes > for masked density like that used to compute CCmask. It may also be worth > looking into the digitization process of "image first" structural biology > methods? > > My question for the BB: can someone explain how Nyquist folding is handled > in cryoEM data processing? > > -James Holton > MAD Scientist > > ######################################################################## > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 > > This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a mailing > list hosted by www.jiscmail.ac.uk, terms & conditions are available at > https://www.jiscmail.ac.uk/policyandsecurity/ > <before_and_after.png> ######################################################################## To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a mailing list hosted by www.jiscmail.ac.uk, terms & conditions are available at https://www.jiscmail.ac.uk/policyandsecurity/
