SIAM Journal on Imaging Sciences最新文献

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An Operator Theory for Analyzing the Resolution of Multi-illumination Imaging Modalities 多照度成像模式分辨率分析的算子理论

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences

Pub Date : 2023-11-15 DOI: 10.1137/23m1551730

Ping Liu, Habib Ammari

SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 2105-2143, December 2023.
Abstract. By introducing a new operator theory, we provide a unified mathematical theory for general source resolution in the multi-illumination imaging problem. Our main idea is to transform multi-illumination imaging into single-snapshot imaging with a new imaging kernel that depends on both the illumination patterns and the point spread function of the imaging system. We therefore prove that the resolution of multi-illumination imaging is approximately determined by the essential cutoff frequency of the new imaging kernel, which is roughly limited by the sum of the cutoff frequency of the point spread function and the maximum essential frequency in the illumination patterns. Our theory provides a unified way to estimate the resolution of various existing super-resolution modalities and results in the same estimates as those obtained in experiments. In addition, based on the reformulation of the multi-illumination imaging problem, we also estimate the resolution limits for resolving both complex and positive sources by sparsity-based approaches. We show that the resolution of multi-illumination imaging is approximately determined by the new imaging kernel from our operator theory and better resolution can be realized by sparsity-promoting techniques in practice but only for resolving very sparse sources. This explains experimentally observed phenomena in some sparsity-based super-resolution modalities.

SIAM影像科学杂志，第16卷，第4期，2105-2143页，2023年12月。摘要。通过引入新的算子理论，为多照度成像问题中一般光源分辨率提供了统一的数学理论。我们的主要思想是将多照度成像转化为单快照成像，并采用一种新的成像核，该核既依赖于照度模式，又依赖于成像系统的点扩展函数。因此，我们证明了多照度成像的分辨率近似由新成像核的基本截止频率决定，而新成像核的基本截止频率大致受点扩展函数的截止频率与照度模式中最大基本频率之和的限制。我们的理论提供了一种统一的方法来估计现有的各种超分辨率模态的分辨率，并得到了与实验结果相同的估计。此外，基于多照度成像问题的重新表述，我们还估计了基于稀疏性的方法解决复杂光源和正光源的分辨率极限。结果表明，基于算子理论的多照度成像分辨率近似由新的成像核决定，而在实际应用中，稀疏度提升技术可以实现更高的分辨率，但仅适用于非常稀疏的光源。这解释了实验中观察到的一些基于稀疏度的超分辨率模式的现象。

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引用次数: 1

Spherical Framelets from Spherical Designs 来自球形设计的球形框架

3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences

Pub Date : 2023-11-14 DOI: 10.1137/22m1542362

Yuchen Xiao, Xiaosheng Zhuang

引用次数: 2

The Split Gibbs Sampler Revisited: Improvements to Its Algorithmic Structure and Augmented Target Distribution 对分离式吉布斯采样器的再考察:改进其算法结构和增强目标分布

3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences

Pub Date : 2023-11-10 DOI: 10.1137/22m1506122

Marcelo Pereyra, Luis A. Vargas-Mieles, Konstantinos C. Zygalakis

Developing efficient Bayesian computation algorithms for imaging inverse problems is challenging due to the dimensionality involved and because Bayesian imaging models are often not smooth. Current state-of-the-art methods often address these difficulties by replacing the posterior density with a smooth approximation that is amenable to efficient exploration by using Langevin Markov chain Monte Carlo (MCMC) methods. An alternative approach is based on data augmentation and relaxation, where auxiliary variables are introduced in order to construct an approximate augmented posterior distribution that is amenable to efficient exploration by Gibbs sampling. This paper proposes a new accelerated proximal MCMC method called latent space SK-ROCK (ls SK-ROCK), which tightly combines the benefits of the two aforementioned strategies. Additionally, instead of viewing the augmented posterior distribution as an approximation of the original model, we propose to consider it as a generalisation of this model. Following on from this, we empirically show that there is a range of values for the relaxation parameter for which the accuracy of the model improves, and propose a stochastic optimisation algorithm to automatically identify the optimal amount of relaxation for a given problem. In this regime, ls SK-ROCK converges faster than competing approaches from the state of the art, and also achieves better accuracy since the underlying augmented Bayesian model has a higher Bayesian evidence. The proposed methodology is demonstrated with a range of numerical experiments related to image deblurring and inpainting, as well as with comparisons with alternative approaches from the state of the art. An open-source implementation of the proposed MCMC methods is available from https://github.com/luisvargasmieles/ls-MCMC.

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引用次数: 1

Sequential Model Correction for Nonlinear Inverse Problems 非线性逆问题的序贯模型校正

3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences

Pub Date : 2023-10-19 DOI: 10.1137/23m1549286

Arttu Arjas, Mikko J. Sillanpää, Andreas S. Hauptmann

引用次数: 0

A Common Lines Approach for Ab Initio Modeling of Molecules with Tetrahedral and Octahedral Symmetry 四面体和八面体对称分子从头建模的公共线方法

3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences

Pub Date : 2023-10-18 DOI: 10.1137/22m150383x

Adi Shasha Geva, Yoel Shkolnisky

A main task in cryo-electron microscopy single particle reconstruction is to find a three-dimensional model of a molecule given a set of its randomly oriented and positioned noisy projection-images. In this work, we propose an algorithm for ab-initio reconstruction for molecules with tetrahedral or octahedral symmetry. The algorithm exploits the multiple common lines between each pair of projection-images as well as self common lines within each image. It is robust to noise in the input images as it integrates the information from all images at once. The applicability of the proposed algorithm is demonstrated using experimental cryo-electron microscopy data.

引用次数: 1

Convolutional Forward Models for X-Ray Computed Tomography x射线计算机断层扫描的卷积正演模型

3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences

Pub Date : 2023-10-12 DOI: 10.1137/21m1464191

Kai Zhang, Alireza Entezari

引用次数: 0

A Data-Assisted Two-Stage Method for the Inverse Random Source Problem 逆随机源问题的数据辅助两阶段法

3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences

Pub Date : 2023-10-12 DOI: 10.1137/23m1562561

Peijun Li, Ying Liang, Yuliang Wang

引用次数: 0

(boldsymbol{L_1-beta L_q}) Minimization for Signal and Image Recovery (boldsymbol{L_1-beta L_q}) 最小化的信号和图像恢复

3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences

Pub Date : 2023-10-11 DOI: 10.1137/22m1525363

Limei Huo, Wengu Chen, Huanmin Ge, Michael K. Ng

The nonconvex optimization method has attracted increasing attention due to its excellent ability of promoting sparsity in signal processing, image restoration, and machine learning. In this paper, we consider a new minimization method and its applications in signal recovery and image reconstruction because minimization provides an effective way to solve the -ratio sparsity minimization model. Our main contributions are to establish a convex hull decomposition for and investigate RIP-based conditions for stable signal recovery and image reconstruction by minimization. For one-dimensional signal recovery, our derived RIP condition extends existing results. For two-dimensional image recovery under minimization of image gradients, we provide the error estimate of the resulting optimal solutions in terms of sparsity and noise level, which is missing in the literature. Numerical results of the limited angle problem in computed tomography imaging and image deblurring are presented to validate the efficiency and superiority of the proposed minimization method among the state-of-art image recovery methods.

非凸优化方法因其在信号处理、图像恢复和机器学习等方面具有提高稀疏性的优异能力而受到越来越多的关注。本文考虑了一种新的最小化方法及其在信号恢复和图像重建中的应用，因为最小化提供了一种有效的方法来解决-比稀疏性最小化模型。我们的主要贡献是建立凸壳分解，并研究基于rip的条件，通过最小化实现稳定的信号恢复和图像重建。对于一维信号恢复，我们推导的RIP条件扩展了已有的结果。对于最小化图像梯度下的二维图像恢复，我们提供了从稀疏度和噪声水平方面得出的最优解的误差估计，这在文献中是缺失的。给出了计算机断层成像和图像去模糊中的极限角度问题的数值结果，验证了该方法在现有图像恢复方法中的有效性和优越性。

引用次数: 0

Subaperture-Based Digital Aberration Correction for Optical Coherence Tomography: A Novel Mathematical Approach 基于子孔径的光学相干层析成像数字像差校正:一种新的数学方法

3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences

Pub Date : 2023-10-11 DOI: 10.1137/22m1543240

Simon Hubmer, Ekaterina Sherina, Ronny Ramlau, Michael Pircher, Rainer Leitgeb

引用次数: 0

Short Communication: Localized Adversarial Artifacts for Compressed Sensing MRI 短通信:压缩感知MRI的局部对抗伪影

3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences

Pub Date : 2023-10-10 DOI: 10.1137/22m1503221

Rima Alaifari, Giovanni S. Alberti, Tandri Gauksson

引用次数: 0

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