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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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This content will become publicly available on December 21, 2025
WTDUN: Wavelet Tree-Structured Sampling and Deep Unfolding Network for Image Compressed Sensing
Deep unfolding networks have gained increasing attention in the field of compressed sensing (CS) owing to their theoretical interpretability and superior reconstruction performance. However, most existing deep unfolding methods often face the following issues: (1) they learn directly from single-channel images, leading to a simple feature representation that does not fully capture complex features; and (2) they treat various image components uniformly, ignoring the characteristics of different components. To address these issues, we propose a novel wavelet-domain deep unfolding framework named WTDUN, which operates directly on the multi-scale wavelet sub-bands. Our method utilizes the intrinsic sparsity and multi-scale structure of wavelet coefficients to achieve a tree-structured sampling and reconstruction, effectively capturing and highlighting the most important features within images. Specifically, the design of tree-structured reconstruction aims to capture the inter-dependencies among the multi-scale sub-bands, enabling the identification of both fine and coarse features, which can lead to a marked improvement in reconstruction quality. Furthermore, a wavelet domain adaptive sampling method is proposed to greatly improve the sampling capability, which is realized by assigning measurements to each wavelet sub-band based on its importance. Unlike pure deep learning methods that treat all components uniformly, our method introduces a targeted focus on important sub-bands, considering their energy and sparsity. This targeted strategy lets us capture key information more efficiently while discarding less important information, resulting in a more effective and detailed reconstruction. Extensive experimental results on various datasets validate the superior performance of our proposed method.
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- Award ID(s):
- 2304489
- PAR ID:
- 10632625
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- ACM Transactions on Multimedia Computing, Communications, and Applications
- Volume:
- 21
- Issue:
- 1
- ISSN:
- 1551-6857
- Page Range / eLocation ID:
- 1 to 22
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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