Multi-target detection with rotations

Bendory, Tamir; Lan, Ti-Yen; Marshall, Nicholas F.; Rukshin, Iris; Singer, Amit

doi:10.3934/ipi.2022046

Cited by 6 publications

(4 citation statements)

References 37 publications

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“…Importantly, it is possible to reconstruct the target volume only up to a 3-D rotation, a 3-D translation, and a reflection. Similar mathematical models were thoroughly studied in previous works for one-and two-dimensional setups [42], [38], [43], [44], [45], [46], [37]. Fig.…”

Section: Measurement Formation Modelmentioning

confidence: 84%

“…Section V discusses how to include additional aspects of the cryo-EM reconstruction problem in the proposed technique, such as the effect of the contrast transfer function (CTF) [47], colored noise, and non-uniform distribution of the rotations of the particles over SO (3). Following previous works [43], [44], we also assume that each translation is separated by at least a full projection length, L, from its neighbors, in both the horizontal and vertical axes. Explicitly, In Section IV-C, we discuss the implications of mitigating this constraint by allowing the projection images to be arbitrarily close.…”

Section: Measurement Formation Modelmentioning

confidence: 99%

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An Approximate Expectation-Maximization for Two-Dimensional Multi-Target Detection

Kreymer

Singer

Bendory

2022

IEEE Signal Process. Lett.

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A single-particle cryo-electron microscopy (cryo-EM) measurement, called a micrograph, consists of multiple two-dimensional tomographic projections of a three-dimensional molecular structure at unknown locations, taken under unknown viewing directions. All existing cryo-EM algorithmic pipelines first locate and extract the projection images, and then reconstruct the structure from the extracted images. However, if the molecular structure is small, the signal-to-noise ratio (SNR) of the data is very low, and thus accurate detection of projection images within the micrograph is challenging. Consequently, all standard techniques fail in low-SNR regimes. To recover molecular structures from measurements of low SNR, and in particular small molecular structures, we devise a stochastic approximate expectation-maximization algorithm to estimate the three-dimensional structure directly from the micrograph, bypassing locating the projection images. We corroborate our computational scheme with numerical experiments, and present successful structure recoveries from simulated noisy measurements.

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Section: Measurement Formation Modelmentioning

confidence: 84%

Section: Measurement Formation Modelmentioning

confidence: 99%

An Approximate Expectation-Maximization for Two-Dimensional Multi-Target Detection

Kreymer

Singer

Bendory

2022

IEEE Signal Process. Lett.

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“…A systematic study of adapting these techniques will be initiated in coming work. Additional future work includes extending the use of sparsifying priors in other parts of the cryo-EM reconstruction pipeline, for instance in existing approaches to iterative refinement ( 25 ) or in autocorrelation analysis using micrographs without particle picking ( 83 – 85 ). However, we do not expect sparsity to have as dramatic an impact on the sample complexity in the case of reconstruction directly from micrographs without particle picking.…”

Section: Discussionmentioning

confidence: 99%

Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms

Bendory

Khoo

Kileel

et al. 2023

Proc. Natl. Acad. Sci. U.S.A.

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The number of noisy images required for molecular reconstruction in single-particle cryoelectron microscopy (cryo-EM) is governed by the autocorrelations of the observed, randomly oriented, noisy projection images. In this work, we consider the effect of imposing sparsity priors on the molecule. We use techniques from signal processing, optimization, and applied algebraic geometry to obtain theoretical and computational contributions for this challenging nonlinear inverse problem with sparsity constraints. We prove that molecular structures modeled as sums of Gaussians are uniquely determined by the second-order autocorrelation of their projection images, implying that the sample complexity is proportional to the square of the variance of the noise. This theory improves upon the nonsparse case, where the third-order autocorrelation is required for uniformly oriented particle images and the sample complexity scales with the cube of the noise variance. Furthermore, we build a computational framework to reconstruct molecular structures which are sparse in the wavelet basis. This method combines the sparse representation for the molecule with projection-based techniques used for phase retrieval in X-ray crystallography.

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“…Unless specified otherwise, we set F = 5 for both algorithms. For the MoM, we minimized the least squares objective (5) using the BFGS algorithm with line-search [43], [44]. The distributions ρ 1 , ρ 2 and their initial guesses were drawn from a uniform distribution on [0, 1], and normalized so that ρ 1 , ρ 2 ∈ L high .…”

Section: Numerical Experimentsmentioning

confidence: 99%

Denoiser-Based Projections for 2D Super-Resolution MRA

Shani,

Tirer,

Giryes

et al. 2024

IEEE Open J. Signal Process.

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We study the 2D super-resolution multi-reference alignment (SR-MRA) problem: estimating an image from its down-sampled, circularly translated, and noisy copies. The SR-MRA problem serves as a mathematical abstraction of the structure determination problem for biological molecules. Since the SR-MRA problem is ill-posed without prior knowledge, accurate image estimation relies on designing priors that describe the statistics of the images of interest. In this work, we build on recent advances in image processing and harness the power of denoisers as priors for images. To estimate an image, we propose utilizing denoisers as projections and using them within two computational frameworks that we propose: projected expectation-maximization and projected method of moments. We provide an efficient GPU implementation and demonstrate the effectiveness of these algorithms through extensive numerical experiments on a wide range of parameters and images.

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Multi-target detection with rotations

Cited by 6 publications

References 37 publications

An Approximate Expectation-Maximization for Two-Dimensional Multi-Target Detection

An Approximate Expectation-Maximization for Two-Dimensional Multi-Target Detection

Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms

Denoiser-Based Projections for 2D Super-Resolution MRA

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