Develops functional multi-target detection theory and recovery algorithms via bispectrum inversion with non-asymptotic guarantees for compactly supported signals under continuous translations and correlated Gaussian noise.
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The first three moments determine generic dihedral orbits in the projected MRA model under high noise via reduction to dihedral phase-coupling, with a constructive scheme and supporting experiments.
Template matching on pure noise yields asymptotic convergence of maximum-likelihood class means and 3D reconstructions to deterministic noise-dependent transforms of the user templates, producing structure-from-noise artifacts.
In low-SNR Gaussian latent-variable models, optimally weighted GMoM using minimal-order moments achieves the same leading asymptotic covariance as MLE via matching layerwise expansions of the information operators.
Functional multi-reference alignment is addressed by extending Kotlarski's deconvolution formula to general dimensions and signals with vanishing Fourier transforms.
citing papers explorer
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Functional Multi-Target Detection via Bispectrum Inversion
Develops functional multi-target detection theory and recovery algorithms via bispectrum inversion with non-asymptotic guarantees for compactly supported signals under continuous translations and correlated Gaussian noise.
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Projected multi-reference alignment
The first three moments determine generic dihedral orbits in the projected MRA model under high noise via reduction to dihedral phase-coupling, with a constructive scheme and supporting experiments.
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Structure from Noise: Confirmation Bias in Particle Picking in Structural Biology
Template matching on pure noise yields asymptotic convergence of maximum-likelihood class means and 3D reconstructions to deterministic noise-dependent transforms of the user templates, producing structure-from-noise artifacts.
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The generalized method of moments is (almost) statistically efficient in low-SNR Gaussian latent-variable models
In low-SNR Gaussian latent-variable models, optimally weighted GMoM using minimal-order moments achieves the same leading asymptotic covariance as MLE via matching layerwise expansions of the information operators.
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Functional Multi-Reference Alignment via Deconvolution
Functional multi-reference alignment is addressed by extending Kotlarski's deconvolution formula to general dimensions and signals with vanishing Fourier transforms.