Two-Dimensional Multi-Target Detection: An Autocorrelation Analysis Approach

Kreymer, Shay; Bendory, Tamir

doi:10.1109/tsp.2022.3147735

Cited by 7 publications

(5 citation statements)

References 36 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%

“…Namely, the set of possible shifts within a patch of all four potential image projections is L 4 , and the space of possible rotations is the group SO(3) × SO(3) × SO(3) × SO(3). A similar analysis was conducted for 1-D [38] and 2-D [45] related models. Clearly, this mechanism will greatly inflate the computational complexity of the algorithm.…”

Section: Arbitrary Spacing Distribution Of Projection Images Within T...mentioning

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: Arbitrary Spacing Distribution Of Projection Images Within T...mentioning

confidence: 99%

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

Kreymer

Singer

Bendory

2022

IEEE Signal Process. Lett.

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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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“…This model is a simplified version of cryo-EM data that, informally speaking, consists of a large noisy measurement that contains many tomographic projections of a 3D density at arbitrary locations and random orientations. While the 2D model we study is not directly applicable to cryo-EM data, it does represent a step towards understanding the application of invariant feature based approaches for cyro-EM by building upon past work on multi-target detection [8,20,21,22,40]. Moreover, the model considered in this paper corresponds to a degenerate case in cryo-EM in which the molecule has a preferred orientation.…”

Section: Motivation and Related Workmentioning

confidence: 99%

“…We mention that our results were recently extended, after this paper appeared online, to account for an arbitrary distribution of the target images [20]. In addition, an approximate expectation-maximization algorithm for the MTD model with rotations was developed in [22,21], and a generalized method of moments framework was designed in [40].…”

Section: Related Workmentioning

confidence: 99%

Multi-target detection with rotations

Bendory

Lan

Marshall

et al. 2022

IPI

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<p style='text-indent:20px;'>We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image. Motivated by single-particle cryo-electron microscopy, we focus on the low signal-to-noise regime, where it is difficult to estimate the locations and orientations of the target images in the measurement. Our approach uses autocorrelation analysis to estimate rotationally and translationally invariant features of the target image. We demonstrate that, regardless of the level of noise, our technique can be used to recover the target image when the measurement is sufficiently large.</p>

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Two-Dimensional Multi-Target Detection: An Autocorrelation Analysis Approach

Cited by 7 publications

References 36 publications

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

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

Denoiser-Based Projections for 2D Super-Resolution MRA

Multi-target detection with rotations

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