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An adaptive Expectation-Maximization algorithm with GPU implementation for electron cryomicroscopy.

ABSTRACT: Maximum-likelihood (ML) estimation has very desirable properties for reconstructing 3D volumes from noisy cryo-EM images of single macromolecular particles. Current implementations of ML estimation make use of the Expectation-Maximization (EM) algorithm or its variants. However, the EM algorithm is notoriously computation-intensive, as it involves integrals over all orientations and positions for each particle image. We present a strategy to speedup the EM algorithm using domain reduction. Domain reduction uses a coarse grid to evaluate regions in the integration domain that contribute most to the integral. The integral is evaluated with a fine grid in these regions. In the simulations reported in this paper, domain reduction gives speedups which exceed a factor of 10 in early iterations and which exceed a factor of 60 in terminal iterations.

SUBMITTER: Tagare HD

PROVIDER: S-EPMC2967204 | biostudies-literature | 2010 Sep

REPOSITORIES: biostudies-literature

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An adaptive Expectation-Maximization algorithm with GPU implementation for electron cryomicroscopy.

Tagare Hemant D HD Barthel Andrew A Sigworth Fred J FJ

Journal of structural biology 20100609 3

Maximum-likelihood (ML) estimation has very desirable properties for reconstructing 3D volumes from noisy cryo-EM images of single macromolecular particles. Current implementations of ML estimation make use of the Expectation-Maximization (EM) algorithm or its variants. However, the EM algorithm is notoriously computation-intensive, as it involves integrals over all orientations and positions for each particle image. We present a strategy to speedup the EM algorithm using domain reduction. Domai ...[more]

PMID: 20538058

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Project description:We are developing a dual modality tomosynthesis breast scanner in which x-ray transmission tomosynthesis and gamma emission tomosynthesis are performed sequentially with the breast in a common configuration. In both modalities projection data are obtained over an angular range of less than 180° from one side of the mildly compressed breast resulting in incomplete and asymmetrical sampling. The objective of this work is to implement and evaluate a maximum likelihood expectation maximization (MLEM) reconstruction algorithm for gamma emission breast tomosynthesis (GEBT).A combination of Monte Carlo simulations and phantom experiments was used to test the MLEM algorithm for GEBT. The algorithm utilizes prior information obtained from the x-ray breast tomosynthesis scan to partially compensate for the incomplete angular sampling and to perform attenuation correction (AC) and resolution recovery (RR). System spatial resolution, image artifacts, lesion contrast, and signal to noise ratio (SNR) were measured as image quality figures of merit. To test the robustness of the reconstruction algorithm and to assess the relative impacts of correction techniques with changing angular range, simulations and experiments were both performed using acquisition angular ranges of 45°, 90° and 135°. For comparison, a single projection containing the same total number of counts as the full GEBT scan was also obtained to simulate planar breast scintigraphy.The in-plane spatial resolution of the reconstructed GEBT images is independent of source position within the reconstructed volume and independent of acquisition angular range. For 45° acquisitions, spatial resolution in the depth dimension (the direction of breast compression) is degraded with increasing source depth (increasing distance from the collimator surface). Increasing the acquisition angular range from 45° to 135° both greatly reduces this depth dependence and improves the average depth dimension resolution from 10.8 to 4.8 mm. The 135° acquisition results in a near-isotropic, spatially uniform 3D resolution of approximately 4.3 mm full width at half maximum. Background nonuniformity (cupping) artifacts arise primarily from angular incompleteness for small angular range acquisition but primarily from gamma ray attenuation at larger angular range. However, background artifacts can be largely eliminated if both prior information regularization and AC are applied. An artificial decrease in lesion voxel value with increasing lesion depth can also be substantially reduced through a combination of AC and RR. In experiments using compressible gelatin breast phantoms, lesion contrast and SNR are about 2.6-8.8 times and 2.3-5.6 times higher, respectively, in GEBT than in planar breast scintigraphy depending on the acquisition angle, the gamma camera trajectory, and the lesion location. In addition, the strong reduction in lesion contrast and SNR with increasing lesion depth that is observed in planar breast scintigraphy can be largely overcome in GEBT.The authors have demonstrated a promising EM-based reconstruction scheme for use in GEBT. Compared to planar breast scintigraphy GEBT provides superior and less position-dependent lesion contrast, lesion SNR, and spatial resolution as well as more accurate quantification of lesion-to-background activity concentration ratio.

Dataset Information

An adaptive Expectation-Maximization algorithm with GPU implementation for electron cryomicroscopy.

Publications

An adaptive Expectation-Maximization algorithm with GPU implementation for electron cryomicroscopy.

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