Model bias in cryo-EM - Einstein from noise

 

 
 
In the article of Maxim Shatsky et al.  entitled "A Method for the Alignment of Heterogeneous Macromolecules from Electron Microscopy" (J Struct Biol. 2009, 166(1): 67–78. doi:10.1016/j.jsb.2008.12.008.), the authors show that pure noise images aligned to a reference image give an average image resembling the reference. This is a perfect example of the model bias occurring during the 2D classification step. Let's do it!!!

Cryo-EM Table of Contents

Section dedicated to Cryo-Electron Microscopy and ImageJ

Normal Map of a sphere using ImageJ

 A small script for creating a normal map of a sphere using ImageJ.

Graphics: Marching Cubes - Results

From the script marchingCubes.js of the previous post [Link], here are some examples of isosurfaces rendered with Blender...

Graphics: Marching Cubes - Implementation

A javascript implementation of the Marching cubes algorithm...

Learning Tomography: Data Collection

Even though this blog is not focused on the experimental devices, it is interesting to have some ideas about the experimental data collection. I created videos to explain the various strategies used in science...

Graphics: Isocontoured Lines

In this series dedicated to 3D rendering, this is a preliminary post describing how to extract vectorial isocontoured lines from an image. One of the most popular algorithm is the Marching Squares algorithm.
The next step will be the computation of isosurfaces...

Learning Tomography: Playing with dots

Last post [Link] was devoted to the problem of rotation center during the reconstruction process. Here is a small exploration of the various patterns that can be observed...

Learning Tomography: Rotation script

In a previous post [Link], I describe artifacts due to non-centered projections in tomography. For those interested, here is the procedure to simulate such a defect in a sinogram.

Learning Tomography: Non-centered projections

Why is my reconstruction so bad ?
This question often arises when the resulting image (or volume) is so disappointing... Specially when you are working with experimental projections, new artifacts and defects are appearing never met before in this series Learning Tomography where all the images are always perfect.
Thus, it is time to show some of these defects... to understand how to fix them.

Learning Tomography: Blur effect

In the simple Back-projection technique, the image appears blurry and we need to pre-filter the sinogram with a ramp filter before computing the 2D reconstruction. Why is this blur effect not observed in the Direct Fourier Reconstruction technique?

3D sample: The Borrromean Rings

In the collection of samples I used for tomography, there is the so-called "Borromean Rings" composed of three interleaved tori [Link].

Learning Tomograhy: New version of back projection

In this series Learning Tomography, I mentioned a backProjImproved.js script in several posts to compute a 2D reconstruction according to the backprojection technique.... Unfortunately, I have never published it. Here it  is...

Learning Tomography: Interpolation in Fourier Rec.

After zero-padding [Link], there is another kind of improvement of our Direct Fourier Reconstruction implementation: The interpolation scheme.
Indeed, during the polar/cartesian conversion, we need to interpolate the sinogram values to exactly fit the cartesian 2D Fourier space. The choice of an interpolation scheme can greatly improve the resulting 2D reconstruction.

Learning Tomography: DFR with Fourier Transform

In this series dedicated to Direct Fourier Reconstruction (DFR), here is a new version based on Discrete Fourier Transform rather than the Hartley Transform...

Learning Tomography: Advanced DFR Implementation

The Direct Fourier Reconstruction (DFR) implementation previously published (Part II:  [Link]) works correctly. However, the polar to cartesian conversion is not very efficient because there are missing pixels in the 2D Fourier space. Modifying the source code can easily fixed this problem...

Learning Tomography: Fourier Rec. in Action

In this (long) series of posts dedicated to Direct Fourier Reconstruction, just a small break with a movie summarizing the steps to compute a 2D reconstruction image...

Learning Tomography: Zero Padding

In the last post [Link], we were able to reconstruct our image. However, the result was encouraging but a little bit disappointing. Fortunately, this can be improved by allowing the computation of Fourier transforms with higher precision.

Learning Tomography: Fourier Rec. - Part II

In this series dedicated to Direct Fourier Reconstruction technique, here is the second (and final) part of the implementation corresponding to the filling of the 2D Fourier space.

Learning Tomography: Fourier Rec. - Part I

First part of this series dedicated to the implementation of Direct Fourier Reconstruction technique: the computation of the Fourier transform of the sinogram.