Article
Engineering, Electrical & Electronic
Amit Vishwakarma
Summary: This article proposes a convolutional sparse representation (CSR)-based method for sonar image denoising and inpainting. The method effectively restores fine details present in sonar images by improving the formation and learning of dictionaries. Experimental results demonstrate that the proposed method outperforms state-of-the-art approaches in terms of visual quality, peak signal-to-noise ratio, and structure similarity.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
(2023)
Article
Computer Science, Artificial Intelligence
Lin Tian, Jiaqing Miao, Xiaobing Zhou, Chao Wang
Summary: This study introduces an image denoising method based on sparse representation, which utilizes adaptive regularization techniques and outperforms other algorithms in terms of PSNR and visual performance.
IET IMAGE PROCESSING
(2021)
Article
Mathematics
Suthep Suantai, Kunrada Kankam, Prasit Cholamjiak
Summary: The study focuses on the convex minimization problem, applies a new algorithm to constrained minimization problems, and outperforms other methods in terms of iterations.
Article
Engineering, Electrical & Electronic
Zhonghua Xie, Lingjun Liu, Cheng Wang
Summary: This paper proposes a novel model-guided boosting framework for improving the restoration quality of image denoising methods. The framework can be flexibly extended to composite denoising and utilizes both external and internal image properties through the use of deep neural networks and low-rank regularization.
Article
Mathematics, Applied
Zakaria Belhachmi, Thomas Jacumin
Summary: We introduce and discuss shape-based models for finding the best interpolation data in the compression of images with noise. The aim is to reconstruct missing regions by minimizing a data fitting term. We analyze the proposed models from two different points of view and provide numerical computations to confirm their usefulness in non-stationary PDE-based image compression.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Computer Science, Artificial Intelligence
Mojtaba Lashgari, Hossein Rabbani, Gerlind Plonka, Ivan Selesnick
Summary: This paper presents a new approach for reconstructing disconnected digital lines based on a constrained regularization model to ensure connectivity in the image plane. The proposed technique improves intersection detection and has potential for fast binary image inpainting.
IEEE TRANSACTIONS ON IMAGE PROCESSING
(2022)
Article
Computer Science, Artificial Intelligence
Ying Wen, Luminita A. Vese, Kehan Shi, Zhichang Guo, Jiebao Sun
Summary: This paper proposes a nonlocal adaptive biharmonic regularization term for image restoration, combining the advantages of fourth-order models and nonlocal methods. The existence and uniqueness of the solution are proved, and the mathematical properties are discussed. Through comparisons with other methods, the advantages of the proposed model are demonstrated.
JOURNAL OF MATHEMATICAL IMAGING AND VISION
(2023)
Article
Engineering, Biomedical
Changfang Chen, Minglei Shu, Shuwang Zhou, Zhaoyang Liu, Ruixia Liu
Summary: In this paper, a group-sparse signal denoising approach is proposed, which incorporates non-convex regularization and sparsity characteristics in the wavelet domain to estimate the electrocardiogram (ECG) signals with noise. A parameterized non-convex penalty function is introduced to strongly promote wavelet sparsity, and the strict convexity of the total cost function is guaranteed by identifying the interval for the parameter. By minimizing a certain single objective function, all the wavelet coefficients are estimated to retain the details of ECG signals and maintain the insignificant coefficients. The effectiveness of the proposed wavelet-domain group-sparse method (WDGS) for ECG signal enhancement is evaluated using real collected ECG signals and the MIT-BIH arrhythmia database through qualitative and quantitative analysis, demonstrating its ability to effectively suppress undesired noise and preserve the important morphology of ECG signals.
BIOMEDICAL SIGNAL PROCESSING AND CONTROL
(2023)
Article
Mathematics, Interdisciplinary Applications
Yuru Zou, Huaxuan Hu, Jian Lu, Xiaoxia Liu, Qingtang Jiang, Guohui Song
Summary: This study introduces a new image denoising model that utilizes both fractal coding and nonlocal self-similarity priors for image compression. Experimental results demonstrate the superior performance of the model in terms of peak-signal-to-noise ratio, structural similarity index and mean absolute error.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(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
Qiuxiang Zhong, Ke Yin, Yuping Duan
Summary: Curvature regularities provide strong priors in edge continuity, but the models are usually non-convex, non-smooth, and highly nonlinear, making numerical computation challenging. This paper estimates discrete mean curvature and Gaussian curvature on a local 3x3 stencil based on fundamental forms in differential geometry, solving a weighted image surface minimization problem efficiently. Numerical experiments show the superiority of the proposed curvature-based model over state-of-the-art variational approaches in image restoration and inpainting.
JOURNAL OF MATHEMATICAL IMAGING AND VISION
(2021)
Article
Engineering, Electrical & Electronic
Chenxin Wang, Zhenwei Zhang, Zhichang Guo, Tieyong Zeng, Yuping Duan
Summary: This paper proposes an efficient and accurate scalar auxiliary variable (SAV) scheme for solving mean curvature and Gaussian curvature minimization problems. The SAV-based algorithms are unconditionally energy diminishing, fast convergent, and very easy to implement for different image applications. Numerical experiments on noise removal, image deblurring, and single image super-resolution demonstrate the robustness and efficiency of our method.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY
(2023)
Article
Engineering, Electrical & Electronic
Xianyu Ge, Jieqing Tan, Li Zhang, Jing Liu, Dandan Hu
Summary: This paper introduces a blind image deblurring method utilizing Gaussian curvature and L-0 norm regularization. By combining these, sharp edges are preserved and detrimental structures and noises are removed in gradual steps, leading to accurate blur kernel estimation and state-of-the-art deblurring results.
SIGNAL PROCESSING-IMAGE COMMUNICATION
(2022)
Article
Computer Science, Information Systems
Ritwik Mukhopadhyay, Prakhar Gupta, Piyush Satti, Bharat Garg
Summary: This paper proposes an Adaptive Radii Selection based Inpainting Method to regenerate the corrupted pixel values caused by Salt & Pepper noise using the Telea Inpainting algorithm. Qualitative and quantitative analysis on standard images and the Kodak image dataset show an improvement in quality metrics such as PSNR by 0.31dB and 8-12% in IEF.
MULTIMEDIA TOOLS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Yiting Chen, Jia Li, Qingyun Yu
Summary: Two re-weighted matching algorithms RWCP and RWWA are proposed in this paper, which enhance the features of missing large regions by inpainting from outside to inside and distance-based weighted average; numerical simulations demonstrate the high applicability of these methods in large region inpainting.
INVERSE PROBLEMS AND IMAGING
(2021)
Review
Mathematics, Applied
Kristian Bredies, Martin Holler
Article
Mathematics, Applied
Kristian Bredies, Silvio Fanzon
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
(2020)
Article
Mathematics, Applied
Sandro Belz, Kristian Bredies
Summary: This paper introduces a new phase field approximation method, in which the phase field is allowed to be a function of bounded variation instead of an H1-function, leading to sharper phase fields compared to traditional methods. This new approximation can be widely used in image segmentation and image processing problems to achieve better results.
ANALYSIS AND APPLICATIONS
(2021)
Article
Computer Science, Theory & Methods
Robert Beinert, Kristian Bredies
Summary: The article introduces a novel algorithm designed to address bilinear and quadratic inverse problems, using tensorial lifting and first-order proximal algorithms for numerical solutions. By deriving tensor-free versions of singular value thresholding methods and employing reweighting techniques, the iterative algorithms show improved convergence behavior and rank evolution. Applied to the two-dimensional masked Fourier phase retrieval problem, the method yields an efficient recovery approach that can incorporate smoothness constraints for enhanced results.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2021)
Article
Mathematics
Kristian Bredies, Marcello Carioni, Silvio Fanzon, Francisco Romero
Summary: This paper characterizes the extremal points of the unit ball of the Benamou-Brenier energy and a generalization of it under the homogeneous continuity equation constraint. It is proven that extremal points are pairs of measures concentrated on absolutely continuous curves, which are characteristics of the continuity equation. This result is then applied to provide a representation formula for sparse solutions of dynamic inverse problems with finite-dimensional data and optimal-transport based regularization.
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2021)
Article
Radiology, Nuclear Medicine & Medical Imaging
Carlos Milovic, Mathias Lambert, Christian Langkammer, Kristian Bredies, Pablo Irarrazaval, Cristian Tejos
Summary: The novel L1-norm data fidelity approach effectively prevents streaking artifacts in QSM reconstructions and is robust against outliers. It demonstrates better performance in testing and does not require the use of additional brain masks.
MAGNETIC RESONANCE IN MEDICINE
(2022)
Article
Computer Science, Artificial Intelligence
Oliver Maier, Stefan M. Spann, Daniela Pinter, Thomas Gattringer, Nicole Hinteregger, Gerhard G. Thallinger, Christian Enzinger, Josef Pfeuffer, Kristian Bredies, Rudolf Stollberger
Summary: A new estimation method for ASL imaging with joint spatial regularization is proposed, enhancing image sharpness and noise suppression. The method is evaluated on synthetic data, healthy volunteers, and patient data, outperforming two reference methods in terms of SNR, sharpness, and quantitative accuracy.
MEDICAL IMAGE ANALYSIS
(2021)
Article
Engineering, Biomedical
Anna Pukaluk, Anna-Sophie Wittgenstein, Gerd Leitinger, Dagmar Kolb, Dominique Pernitsch, Sarah A. Schneider, Patrick Knoebelreiter, Verena Horak, Kristian Bredies, Gerhard A. Holzapfel, Thomas Pock, Gerhard Sommer
Summary: This study offers a method to investigate the arrangement of collagen fibrils and proteoglycans in the mechanically loaded aortic wall. The 3D reconstructions reveal a complex organization of collagen fibrils and PGs and provide insights into the ultrastructural changes caused by mechanical stimuli. This method has significant implications for understanding the response of soft biological tissues to mechanical loading.
ACTA BIOMATERIALIA
(2022)
Article
Computer Science, Theory & Methods
Kristian Bredies, Marcello Carioni, Silvio Fanzon, Francisco Romero
Summary: We propose a dynamic generalized conditional gradient method for dynamic inverse problems with optimal transport regularization. The method effectively reconstructs heavily undersampled dynamic data and demonstrates convergence and optimization performance.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2023)
Article
Mathematics, Applied
Kristian Bredies, Marcello Carioni, Martin Holler
Summary: We introduce and study a mathematical framework called regularization graphs for a broad class of regularization functionals. This framework allows for the construction of regularization methods and covers existing approaches while also allowing for flexibility in creating new ones. Well-posedness and convergence results are provided, and a bilevel optimization approach is presented to learn optimal weights for the regularization graphs.
Article
Mathematics, Applied
Kristian Bredies, Marcello Carioni, Silvio Fanzon
Summary: This study investigates measure-valued solutions of the inhomogeneous continuity equation with low regularity coefficients. A new superposition principle is proven for positive measure solutions and coefficients with finite dynamic Hellinger-Kantorovich energy. This principle provides a decomposition of the solution into curves that satisfy the characteristic system in an appropriate sense and generalizes existing superposition principles to cases with low-regularity coefficients.
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Kristian Bredies, Enis Chenchene, Dirk A. Lorenz, Emanuele Naldi
Summary: This paper presents a systematic procedure for analyzing the convergence of degenerate preconditioned proximal point algorithms. Weak convergence results are established under mild assumptions, which can be easily applied to splitting methods for monotone inclusion and convex minimization problems. The degeneracy of the preconditioner allows for a reduction in the variables involved in iteration updates. The proposed framework demonstrates its strength in the context of splitting algorithms, providing simplified proofs of convergence and highlighting the connection between existing schemes from a preconditioned proximal point perspective.
SIAM JOURNAL ON OPTIMIZATION
(2022)
Article
Mathematics, Applied
Kristian Bredies, Jose A. Iglesias, Gwenael Mercier
Summary: The paper investigates whether the minimizers of total variation regularization in linear inverse problems belong to L-8 space, even if the measured data does not. It presents a simple proof of boundedness for the minimizer with a fixed regularization parameter and derives the existence of uniform bounds under certain conditions. The paper also discusses the limitation of these results and proposes the possibility of extending them to higher-order regularization functionals.
APPLIED MATHEMATICS AND OPTIMIZATION
(2023)
Article
Computer Science, Software Engineering
Kristian Bredies, Marcello Carioni, Silvio Fanzon, Daniel Walter
Summary: We propose a fully-corrective generalized conditional gradient method (FC-GCG) for minimizing the sum of a smooth, convex loss function and a convex one homogeneous regularizer over a Banach space. The algorithm updates a finite set Ak of extremal points of the regularizer's unit ball and an iterate uk ? cone(Ak). Each iteration involves solving a linear problem to update Ak and a finite-dimensional convex minimization problem to update the iterate. We prove that under standard hypotheses, the algorithm converges sublinearly and can achieve a linear rate of convergence with additional assumptions on the dual variables using Choquet's theorem and the Primal-Dual-Active-Point method.
MATHEMATICAL PROGRAMMING
(2023)
Article
Mathematics, Applied
Kristian Bredies, Richard Huber
Summary: This paper introduces a novel mathematical framework for understanding pixel-driven approaches for the parallel beam Radon transform and fanbeam transform, demonstrating that convergence can be achieved with the correct discretization strategy. The study shows that setting the pixel resolution in the Radon transform to be asymptotically smaller than the detector size leads to convergence, and discusses possible adjustments for limited-angle and sparse-angle Radon transforms. In addition, the convergence results are extended to a new pixel-driven approach for the fanbeam transform, emphasizing the importance of correct discretization strategies in avoiding high-frequency artifacts.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2021)
