A major challenge in single particle reconstruction from cryo electron-microscopy is to establish a reliable ab-initio 3D model using 2D images with unknown orientations. Common-lines based methods can determine the orientations of images without additional geometric information. However, such methods fail when the detection rate of common-lines is too low due to the high level of noise in the images. An approximation to the least squares global self consistency error was obtained using convex relaxation by semidefinite programming. The purpose of this paper is three-fold. First, we introduce another, yet more robust , global self consistency error in an optimization problem that can be solved via semidefinite relaxation. Second, we introduce a spectral norm constraint to robustify the relaxed problem. Third, we use alternating direction method or the iteratively reweighted least squares (IRLS) procedureto solve the problem . Numerical experiments  demonstrate that the proposed method significantly decreases the orientation estimation error when the detection rate of common-lines is low.
A major challenge in single particle reconstruction from cryo-electron microscopy is to establish a reliable ab-initio three-dimensional model using two-dimensional projection images with unknown orientations. Common-lines based methods estimate the orientations without additional geometric information. However, such methods fail when the detection rate of common-lines is too low due to the high level of noise in the images. An approximation to the least squares global self consistency error was obtained using convex relaxation by semidefinite programming. In this paper we introduce a more robust global self consistency error and show that the corresponding optimization problem can be solved via semidefinite relaxation. In order to prevent artificial clustering of the estimated viewing directions, we further introduce a spectral norm term that is added as a constraint or as a regularization term to the relaxed minimization problem. The resulted problems are solved by using either the alternating direction method of multipliers or an iteratively reweighted least squares procedure . Numerical experiments with both simulated and real images demonstrate that the proposed methods significantly reduce the orientation estimation error when the detection rate of common-lines is low.
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cryo electron-microscopy
cryo-electron microscopy
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3D model using 2D
three-dimensional model using two-dimensional projection
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can determine the orientations of images
estimate the orientations
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The purpose of this paper is three-fold. First, we introduce another, yet more robust ,
In this paper we introduce a more robust
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in an optimization problem that
and show that the corresponding optimization problem
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Second, we
In order to prevent artificial clustering of the estimated viewing directions, we further
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constraint to robustify the relaxed problem. Third, we use
term that is added as a constraint or as a regularization term to the relaxed minimization problem. The resulted problems are solved by using either the
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or the
of multipliers or an
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(IRLS) procedureto solve the problem
procedure
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with both simulated and real images
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method significantly decreases
methods significantly reduce