Radial Function Based Ab-Initio Tomographic Reconstruction for Cryo Electron Microscopy

Michels, Yves; Baudrier, Étienne; Mazo, Laic

doi:10.1109/icip.2018.8451792

Cited by 2 publications

(4 citation statements)

References 11 publications

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“…Likewise, GMMs are also useful for representing lower resolution, or coarsegrained, 3D cryo-EM images of bio-molecules. In this connection, mixtures of a pre-set number of isotropic Gaussians were employed for 3D-EM reconstruction in [JH15,MBM18]. Moreover, sparse representations by GMMs are often used for post-processing of 3D-EM reconstructions [JS15,Kaw18].…”

Section: Gaussian Mixture Models Of Signals and Their Ray Transformmentioning

confidence: 99%

Joint Gaussian dictionary learning and tomographic reconstruction

Zickert

Öktem²,

Yarman³

2022

Inverse Problems

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This paper studies ill-posed tomographic imaging problems where the image is sparsely represented by a non-negative linear combination of Gaussians. Our main contribution is to develop a scheme for directly recovering the Gaussian mixture representation of an image from tomographic data, which here is modeled as noisy samples of the parallel-beam ray transform. An important aspect of this non-convex reconstruction problem is the choice of initial guess. We propose a procedure for initializations that is based on a filtered back projection type of operator tailored for the Gaussian dictionary. This operator can be evaluated efficiently using an approximation of the Riesz-potential of an anisotropic Gaussian which is based on an exact closed form expression for the Riesz-potential of an isotropic Gaussian. The proposed method is evaluated on simulated data.

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Section: Gaussian Mixture Models Of Signals and Their Ray Transformmentioning

confidence: 99%

Joint Gaussian dictionary learning and tomographic reconstruction

Zickert

Öktem²,

Yarman³

2022

Inverse Problems

View full text Add to dashboard Cite

show abstract

“…Moreover, methods based on projection-matching were found to degrade significantly in low SNR regimes [20] or when errors occur in the estimation of the density map used for the generation of the clean templates [21]. Examples of joint-reconstruction methods that address 3D ab initio modeling are found in [22], [23]. In [22], a frequencymarching approach that increases the resolution of the reconstruction is proposed.…”

Section: A Standard 3d Refinement Techniquesmentioning

confidence: 99%

“…This leads to a smaller computational overhead in projection-matching steps. In [23], the density map parameters are updated through gradient descent while the projection orientations are recovered through exhaustive search on an SO(3) grid, followed by convex optimization. Although they provide efficient 3D ab initio modeling, these methods still suffer from the shortcomings of projection-matching.…”

Section: A Standard 3d Refinement Techniquesmentioning

confidence: 99%

See 1 more Smart Citation

Joint Angular Refinement and Reconstruction for Single-Particle Cryo-EM

Zehni

Donati

Soubies

et al. 2020

IEEE Trans. on Image Process.

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Single-particle cryo-electron microscopy (cryo-EM) reconstructs the three-dimensional (3D) structure of biomolecules from a large set of 2D projection images with random and unknown orientations. A crucial step in the single-particle cryo-EM pipeline is 3D refinement, which resolves a highresolution 3D structure from an initial approximate volume by refining the estimation of the orientation of each projection. In this work, we propose a new approach that refines the projection angles on the continuum. We formulate the optimization problem over the density map and the orientations jointly. The density map is updated using the efficient alternating-direction method of multipliers, while the orientations are updated through a semicoordinate-wise gradient descent for which we provide an explicit derivation of the gradient. Our method eliminates the requirement for a fine discretization of the orientation space and does away with the classical but computationally expensive templatematching step. Numerical results demonstrate the feasibility and performance of our approach compared to several baselines.

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Radial Function Based Ab-Initio Tomographic Reconstruction for Cryo Electron Microscopy

Cited by 2 publications

References 11 publications

Joint Gaussian dictionary learning and tomographic reconstruction

Joint Gaussian dictionary learning and tomographic reconstruction

Joint Angular Refinement and Reconstruction for Single-Particle Cryo-EM

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