Article
Mathematical & Computational Biology
Xiaolei Gu, Wei Xue, Yanhong Sun, Xuan Qi, Xiao Luo, Yongsheng He
Summary: This paper proposes a model called the isotropic total variation regularized least absolute deviations measure (LADTV) for magnetic resonance image deblurring and denoising. The model utilizes the least absolute deviations term to measure the violation of the relationship between the desired magnetic resonance image and the observed image, and to suppress noise. It also incorporates an isotropic total variation constraint to preserve the smoothness of the desired image. Experimental results on clinical data demonstrate the effectiveness of the proposed approach.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Engineering, Electrical & Electronic
Ezgi Demircan-Tureyen, Mustafa E. Kamasak
Summary: A two-stage denoising framework was proposed for adaptive denoising using direction descriptors to guide structure tensor, enhancing sensitivity of STV. By efficiently capturing local geometry with a preprocessor, experiments demonstrate the benefits of incorporating directional information into STV.
SIGNAL PROCESSING-IMAGE COMMUNICATION
(2021)
Article
Mathematics, Applied
Jingjing Liu, Ruijie Ma, Xiaoyang Zeng, Wanquan Liu, Mingyu Wang, Hui Chen
Summary: Non-convex total variation is proposed for image deblurring and denoising model by combining non-convex regularization and non-convex data fitting terms, enhancing sensitivity to sharp edges and object boundaries. The optimization method based on ADMM is efficient, with subproblems having closed-form solutions or being solved by fast solvers. The proposed model outperforms existing convex and non-convex total variation models.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Computer Science, Software Engineering
Wen-Ze Shao, Hai-Song Deng, Wei-Wei Luo, Jin-Ye Li, Mei-Lin Liu
Summary: This paper introduces a new image prior called reweighted graph total variation (RGTV), which has been shown to outperform classical total variation (TV) and other cutting-edge models in blind deconvolution. The paper also explores the potential of RGTV in blind facial image restoration, achieving promising results by combining unsupervised deep facial models.
Article
Mathematics
Shahid Saleem, Shahbaz Ahmad, Junseok Kim
Summary: Ensuring non-negative restored intensities is crucial in image deblurring, but current numerical techniques often produce negative intensities resulting in dark areas. To address this, we propose a mathematical model based on total fractional-order variational principles that guarantees positive intensities within a specified range. We introduce numerical algorithms and a circulant preconditioned matrix to overcome convergence issues. Computational tests validate the effectiveness of our approach in practical applications.
Article
Mathematics, Applied
Lin Guo, Xi-Le Zhao, Xian-Ming Gu, Yong-Liang Zhao, Yu-Bang Zheng, Ting-Zhu Huang
Summary: Researching efficient image deblurring methods remains a challenge, as current approaches based on integer-order derivatives have drawbacks. A new three-dimensional fractional total variation (3DFTV) model is proposed to address these issues and experimental results show its superiority in quality metrics and visual effects compared to existing models.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Operations Research & Management Science
Pasquale Cascarano, Giorgia Franchini, Erich Kobler, Federica Porta, Andrea Sebastiani
Summary: Deep Image Prior (DIP) is an efficient unsupervised deep learning method for ill-posed inverse problems in imaging. It relies on generative CNN architectures and has shown robustness in denoising and deblurring tasks on simulated and real images.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2023)
Article
Computer Science, Artificial Intelligence
Antonin Chambolle, Thomas Pock
Summary: This work introduces a general framework for discrete approximations of total variation in image reconstruction, showing consistency in the sense of Gamma-convergence. Algorithms for learning discrete total variation are proposed to achieve optimal reconstruction quality for specific image reconstruction tasks. The study reveals significant differences in learned discretizations for different tasks, indicating that there is no universal best discretization method for total variation.
SIAM JOURNAL ON IMAGING SCIENCES
(2021)
Article
Mathematics, Applied
Konstantinos Bessas
Summary: We study a nonlocal version of the total variation-based model with L1 fidelity for image denoising, where the regularizing term is replaced with the fractional s-total variation. We discuss the regularity of the level sets and uniqueness of solutions for both high and low values of the fidelity parameter. We analyze in detail the case of binary data given by the characteristic functions of convex sets.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Engineering, Electrical & Electronic
Reza Parvaz
Summary: This paper introduces the burgeoning subject of restoring images corrupted by noise and blur in image processing. Fractional derivatives are used as a powerful tool for this purpose, combined with fractional-order total variation and framelet transform to improve the nonconvex model for image restoration with impulse noise problem. The proposed model is solved using the alternating direction method of multipliers (ADMM) and primal-dual problem. The convergence of the algorithm is studied, and the algorithm is evaluated using different types of tests.
SIGNAL IMAGE AND VIDEO PROCESSING
(2023)
Article
Geochemistry & Geophysics
Shingo Takemoto, Kazuki Naganuma, Shunsuke Ono
Summary: The spatio-spectral total variation (SSTV) model is widely used for regularization of hyperspectral images (HSIs), but it struggles with removing noise while preserving complex spatial structures. To address this issue, we propose a new regularization method called graph-SSTV (GSSTV), which explicitly reflects the spatial structure of the HSI and incorporates a weighted spatial difference operator. We formulate the noise removal problem as a convex optimization problem involving GSSTV and develop an efficient algorithm to solve it.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS
(2022)
Article
Geochemistry & Geophysics
Yang Chen, Wenfei Cao, Li Pang, Jiangjun Peng, Xiangyong Cao
Summary: The TV regularizer is commonly used in image-processing tasks but weakens the texture structure of an image. To address this issue, we propose a texture-preserved TV regularizer for HSIs by introducing a weighting scheme to relax the sparsity constraint for pixels with large variations. We also present an empirical method to adaptively learn the weights from observed HSIs. Experimental results demonstrate the superiority of our proposed method in HSI denoising and the improved performance after embedding the weighting scheme in the original method.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2023)
Article
Optics
Jiali Yao, Dalong Qi, Yunhua Yao, Fengyan Cao, Yilin He, Pengpeng Ding, Chengzhi Jin, Tianqing Jia, Jinyang Liang, Lianzhong Deng, Zhenrong Sun, Shian Zhang
Summary: A total variation (TV) combined with block matching and 3D filtering (BM3D) reconstruction algorithm is proposed to improve the image quality of Compressed Ultrafast Photography (CUP), named as TV-BM3D algorithm. This algorithm exploits gradient sparsity and non-local similarity for image reconstruction, showing better performance compared to conventional algorithms in terms of image quality and noise immunity in CUP.
OPTICS AND LASERS IN ENGINEERING
(2021)
Article
Engineering, Electrical & Electronic
Kaicong Sun, Sven Simon
Summary: This paper proposes a regularization technique named bilateral spectrum weighted total variation (BSWTV) to address the oversmoothness and residual noise issues in noisy-image super-resolution and image denoising. By introducing locally adaptive shrink coefficient and eigenvalues of the covariance matrix, the weighting map is effectively refined to suppress the residual noise and improve image quality.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Chemistry, Multidisciplinary
Antonio Boccuto, Ivan Gerace, Valentina Giorgetti
Summary: This paper focuses on reducing the computational cost of a GNC Algorithm for deblurring images when dealing with full symmetric Toeplitz block matrices composed of Toeplitz blocks. The analysis in this paper centers around the class of gamma matrices, which can perform vector multiplications quickly. The proposed approach involves adding a minimization step for a new approximation of the energy function to the GNC technique. The experimental results demonstrate that the new GNC algorithm proposed in this paper reduces computation time by over 20% compared with its previous version, while maintaining the same image reconstruction quality.
APPLIED SCIENCES-BASEL
(2023)
Article
Mathematics, Applied
Lukas F. Lang, Sebastian Neumayer, Ozan Oktem, Carola-Bibiane Schonlieb
APPLIED MATHEMATICS AND OPTIMIZATION
(2020)
Article
Mathematics, Applied
Volker Grimm
Article
Computer Science, Artificial Intelligence
Stephen Marsland, Robert I. McLachlan, Raziyeh Zarre
Summary: This study discusses the use of finite-dimensional planar Lie groups for image registration to aid in understanding changes such as growth and atrophy, and describing them in a linear space. The selection of appropriate Lie groups can be made using model selection, with groups having the smallest number of parameters preferred.
JOURNAL OF MATHEMATICAL IMAGING AND VISION
(2021)
Article
Computer Science, Artificial Intelligence
Angelica I. Aviles-Rivero, Noemie Debroux, Guy Williams, Martin J. Graves, Carola-Bibiane Schonlieb
Summary: This work presents a new framework for dynamic MRI reconstruction using a multi-task optimization model called Compressed Sensing Plus Motion, which simultaneously computes MRI reconstruction and physical motion. The proposed approach demonstrates potentials and advantages in various clinical applications.
MEDICAL IMAGE ANALYSIS
(2021)
Article
Mathematics, Applied
E. Celledoni, M. J. Ehrhardt, C. Etmann, R. Mclachlan, B. Owren, C-B Schonlieb, F. Sherry
Summary: Deep learning has become a topic of massive interest due to successes in large-scale image processing tasks. However, applying deep learning involves solving challenging mathematical problems and understanding the trade-off between computational effort, data amount, and model complexity. Progress in deep learning has been based on heuristic explorations, but there is a growing effort to mathematically understand existing methods and design new ones with certain structures.
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Jonas Adler, Sebastian Lunz, Olivier Verdier, Carola-Bibiane Schonlieb, Ozan Oktem
Summary: This paper discusses how to perform a post-processing task on a model parameter in an ill-posed inverse problem, where the parameter is only indirectly observed through noisy data. The authors propose a framework based on (deep) neural networks to formalize the reconstruction and post-processing steps as statistical estimation problems. By jointly training the networks against suitable supervised training data, an end-to-end task adapted reconstruction method is obtained. The suggested framework is generic and adaptable, allowing for customization of the inverse problem and post-processing task. The approach is demonstrated on joint tomographic image reconstruction, classification, and segmentation.
Article
Mathematics, Applied
Elena Celledoni, Matthias J. Ehrhardt, Christian Etmann, Brynjulf Owren, Carola-Bibiane Schonlieb, Ferdia Sherry
Summary: The use of convolutional layers to encode an inductive bias in neural networks has proven to be fruitful, leading to research into incorporating other symmetries. This work shows that group equivariant convolutional operations can be integrated into learned reconstruction methods, improving quality without additional costs.
Article
Mathematics, Applied
Timothee Schmoderer, Angelica Aviles-Rivero, Veronica Corona, Noemie Debroux, Carola-Bibiane Schonlieb
Summary: The study introduces a new mathematical model for reconstructing high-quality medical MRI from few measurements by combining compressed sensing formulation and optical flow motion compensation. The proposed approach demonstrates advanced capabilities in dynamic MRI reconstruction through an efficient optimization scheme and multi-tasking reconstruction techniques.
Editorial Material
Engineering, Electrical & Electronic
Subhadip Mukherjee, Andreas Hauptmann, Ozan Oktem, Marcelo Pereyra, Carola-Bibiane Schonlieb
Summary: In recent years, there has been significant progress in understanding the stability and convergence of data-driven methods for image reconstruction, despite concerns about their lack of robustness. This article introduces convergence concepts and presents a survey of learned methods with mathematically rigorous guarantees, such as input-convex neural networks (ICNNs) that combine deep learning with convex regularization theory. The article aims to provide valuable insights for methodological researchers and practitioners alike, by advancing the understanding and establishing a solid mathematical foundation for data-driven image reconstruction.
IEEE SIGNAL PROCESSING MAGAZINE
(2023)
Article
Engineering, Electrical & Electronic
Dongdong Chen, Mike Davies, Matthias J. Ehrhardt, Carola-Bibiane Schonlieb, Ferdia Sherry, Julian Tachella
Summary: From early image processing to modern computational imaging, successful models and algorithms have relied on the fundamental property of natural signals: symmetry. Symmetry, in the form of equivariance, can also be incorporated into deep neural networks (DNNs) for more data-efficient learning. However, computational imaging presents unique challenges for equivariant network solutions due to the observation of images through noisy and ill-conditioned operators. The emerging field of equivariant imaging (EI) provides improved generalization and new imaging opportunities, with links to acquisition physics, iterative reconstruction, blind compressed sensing, and self-supervised learning.
IEEE SIGNAL PROCESSING MAGAZINE
(2023)
Article
Mathematics, Applied
Carlos Esteve-Yague, Willem Diepeveen, Ozan Oktem, Carola-Bibiane Schonlieb
Summary: This paper presents the problem of reconstructing the three-dimensional atomic structure of a flexible macromolecule from a cryogenic electron microscopy (cryo-EM) dataset. By assuming that the macromolecule can be modeled as a chain or discrete curve, a method is introduced to estimate the deformation of the atomic model with respect to a given conformation. The method involves estimating the torsion and bond angles of the atomic model in each conformation as a linear combination of the eigenfunctions of the Laplace operator in the manifold of conformations.
Article
Engineering, Biomedical
Malena Sabate Landman, Ander Biguri, Sepideh Hatamikia, Richard Boardman, John Aston, Carola-Bibiane Schonlieb
Summary: Krylov subspace methods are powerful iterative solvers for linear systems, commonly used in inverse problems. This work aims to bridge the gap between this field and applied medical physics and engineering, by providing a general framework for relevant Krylov subspace methods applied to 3D CT problems. Numerical results in synthetic and real-world CT applications are presented to showcase and compare the different methods.
PHYSICS IN MEDICINE AND BIOLOGY
(2023)
Article
Computer Science, Interdisciplinary Applications
Yiran Wei, Xi Chen, Lei Zhu, Lipei Zhang, Carola-Bibiane Schonlieb, Stephen Price, Chao Li
Summary: The proposed study presents a multi-modal learning framework for predicting the genotype of glioma by integrating focal tumor image, tumor geometrics, and global brain network features. Experimental results demonstrate that the model outperforms baseline deep learning models, and the visualized interpretation aligns with clinical knowledge.
IEEE TRANSACTIONS ON MEDICAL IMAGING
(2023)
Article
Computer Science, Information Systems
Lei Zhu, Xiaoqiang Wang, Ping Li, Xin Yang, Qing Zhang, Weiming Wang, Carola-Bibiane Schonlieb, C. L. Philip Chen
Summary: RGB-D salient object detection aims to detect visually distinctive objects or regions from a pair of the RGB image and the depth image. In this work, we propose a self-supervised self-ensembling network (S-3 Net) for semi-supervised RGB-D salient object detection by leveraging the unlabeled data and exploring a self-supervised learning mechanism. Experimental results demonstrate that our network outperforms the state-of-the-art methods on seven widely-used benchmark datasets.
IEEE TRANSACTIONS ON MULTIMEDIA
(2023)
Article
Computer Science, Artificial Intelligence
Philip Sellars, Angelica Aviles-Rivero, Carola-Bibiane Schonlieb
Summary: Semisupervised learning has gained attention for its ability to reduce the need for labeled data and improve deep semisupervised classification performance. This paper introduces the LaplaceNet framework, which utilizes graph-based pseudolabels and neural network training to achieve state-of-the-art results. The use of multisampling augmentation also enhances generalization.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
