Hi there!
First of all, this isn’t really a feature request but more of a question and, hopefully, opening for discussion. Basically, I’ve lately been pondering how to handle anisotropic particle distributions due to strongly preferred orientations. In such cases, theoretically, the optimal outcome would - as I see it - be either an anisotropic, clean map or a low-passed filtered version of the former to create an isotropic map of lower resolution. However, because alignment is done in spheres in Fourier space, what usually comes out (for me at least) is an anisotropic map to lower degree (higher sphericity) than present in the data (when comparing to 2D FRCs) but with overfitting in the poorly resolved planes. Is it, at a theoretical level, conceivable to do the alignment in ellipses in Fourier space based on directional FSCs, which would almost guarantee an anisotropic map but without the overfitting in directions of lower resolution? I picture this basically as NU-refine with regularisation in Fourier space, if that makes any sense. I’m interested in hearing if anyone has thoughts on whether this is theoretically possible, or if it would violate some basic assumptions of refinement, but also in the computational feasibility of this, as I’m sure calculating directional FSCs is much heavier than one global FSC. Also, I’m not even sure how much people would use it, as having prohibitively preferred orientation usually shows up quite early in processing, and maybe people mostly abandon processing at that stage and go back to grid optimisation?
I’m looking forward to hearing some thoughts!
Sincerely, Martin
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We do not abandon processing at that point…
We live or die on that battlefield 
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Hehe, yeah, that’s how we currently approach it as well. A noticeably anisotropic map would probably never be very publishable, but it can be super useful to convince PI/facility that it’s worth pursuing the needle in the haystack of grid optimisation!
Hi @au583982,
This is an interesting topic, thanks for raising it for discussion! Could you clarify what you mean by doing “alignment in ellipses in Fourier space based on directional FSCs”? Anisotropic-based map regularization is an area we’ve been keen on exploring, but it’s not immediately clear to us how to use directional FSC tools like 3DFSC to generate an anisotropic density regularization algorithm. It’s also not clear to us if directional FSCs are the best tool to try to base an anisotropic regularization procedure on, or if they are better for diagnosing the problem only.
In practice, another question is how useful such an algorithm could be. If we regularize anisotropically, while this may help prevent overfitting along poorly resolved planes, it’s unclear if this would still help get to a passable density map in the case of strong preferred orientation – especially if such an algorithm just suppresses higher frequencies in the poor directions.
Best,
Michael
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In practice, another question is how useful such an algorithm could be. If we regularize anisotropically, while this may help prevent overfitting along poorly resolved planes, it’s unclear if this would still help get to a passable density map in the case of strong preferred orientation – especially if such an algorithm just suppresses higher frequencies in the poor directions.
Maybe the best way to answer this would be using synthetic data - make synthetic datasets with particles that have known orientations and a certain degree of preferred orientation, then compare a direct reconstruction (with ground truth orientations) to a refinement (where orientations are initially discarded). Wouldn’t even need synthetic data really - could take an existing EMPIAR set and just remove data along one direction.
I suspect that some form of directional regularization (maybe local, to account for anisotropy introduced by interdomain flexibility) will help to some degree, but not sure what the best way to approach it would be…
Sure, I’m glad you think it’s a discussion worth having!
As I mentioned, I’m not very well-versed in the backend math, so my thinking may very well be flawed, but it goes along the lines of this:
During any 3D refinement, the resolution of the particle data that is used for refinement starts at the initial low-pass frequency and increases gradually by employing some kind of filter with increasing transition point. This should correspond to some kind of soft, spherical mask in Fourier space with increasing radius. If the filter could be defined such that this soft mask in Fourier space is not spherical but instead an ellipsoid with semi-axes determined by directional FSCs, then high-resolution information in well-represented orientations could be kept, while the same resolution in poorer orientations would be filtered out. (I suspect a very coarse directional sampling of maybe 45 degrees should be plenty.)
As far as I can imagine, if you have any good orientation, this would mean a disk of large radius in Fourier space and so it should only be necessary to have one semi-axis being shorter than the others, but I might be missing something obvious.
My thoughts are partly inspired by a dataset I’m currently processing (granted, it has a handful of other pathologies) where I stalled around 8 Å with an initial untilted data collection but by injecting a dataset at 25 degrees tilt just 10% the size of the untilted, I could go on to ~6 Å, also when I subsequently removed the tilted particles and did local refinement with the default pose priors. Since I also did all sorts of other things in between, it could be that it was due to something else, but it made me think that maybe the initial, limiting factor was overfitting in the poor direction.
Sincerely, Martin
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