Sparse object supports are often encountered in many imaging problems. For such sparse objects, recent theory
of compressed sensing tells us that accurate reconstruction of objects are possible even from highly limited
number of measurements drastically smaller than the Nyquist sampling limit by solving L1 minimization problem.
This paper employs the compressed sensing theory for cryo-electron microscopy (cryo-EM) single particle
reconstruction of virus particles. Cryo-EM single particle reconstruction is a nice application of the compressed
sensing theory because of the following reasons: 1) in some cases, due to the difficulty in sample collection, each
experiment can obtain micrographs with limited number of virus samples, providing undersampled projection
data, and 2) the nucleic acid of a viron is enclosed within capsid composed of a few proteins; hence the support
of capsid in 3-D real space is quite sparse. In order to minimize the L1 cost function derived from compressed
sensing, we develop a novel L1 minimization method based on the sliding mode control theory. Experimental
results using synthetic and real virus data confirm that the our algorithm provides superior reconstructions of
3-D viral structures compared to the conventional reconstruction algorithms.
In the cryo-EM tomography, the projection and back-projection are essential steps in reconstruction the 3D structure of the virus and macromolecules. Distance driven method (DD) is the latest projection /backprojection algorithm originally employed for x-ray computed tomography. This paper is mainly concerned about employing this algorithm to the cryo-EM tomography for reconstruction performance improvement. Existing algorithms used in cryo-EM are pixel-driven and ray driven projection/backprojection, etc. These methods are generally quite time consuming because of their high computational complexity. Furthermore, interpolation artifacts are usually noticeable when the sufficient view and detector samples are not available. The DD is originally proposed to overcome these drawbacks. The interpolation process in DD is done by calculating the overlap area between the detector and pixel boundaries. This procedure largely removes the interpolation artifacts, and reduces the computational complexity significantly. Furthermore, it guarantees that the projection and backprojection are adjoint to each other - a desired property to guarantee the convergence of the iterative reconstruction algorithm. However, unlike the x-ray computed tomography, the cryo-EM tomography problem generally has limited number of the projections, and projection angles are randomly distributed over 4pi steradian. Therefore, the conventional DD should be modified. Rather than computing the boundary overlap in the previous 3-D DD method, we propose a novel DD algorithm based on volume overlap. CCMV virus model is used as testing example. Results are visualized using AMIRA software. Analysis is made upon the advantages and drawbacks of both the existing approaches and distance driven method.
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