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Congratulations to IPI Editor in Chief Gunther Uhlmann on winning the 2021 George Birkhoff Prize in Applied Mathematics for his fundamental and insightful contributions to inverse problems and partial differential equations, as well as for his incisive work on boundary rigidity, microlocal analysis and cloaking. Learn more about the award and Dr. Uhlmann's achievements on the AMS website.

Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing.

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IPI special issue on "mathematical/statistical approaches in data science" in the Inverse Problem and Imaging
Weihong Guo, Yifei Lou, Jing Qin and Ming Yan
2021, 15(1) : I-I doi: 10.3934/ipi.2021007 +[Abstract](158) +[HTML](66) +[PDF](76.17KB)
Reproducible kernel Hilbert space based global and local image segmentation
Liam Burrows, Weihong Guo, Ke Chen and Francesco Torella
2021, 15(1) : 1-25 doi: 10.3934/ipi.2020048 +[Abstract](542) +[HTML](273) +[PDF](5192.41KB)
Automatic extraction of cell nuclei using dilated convolutional network
Rajendra K C Khatri, Brendan J Caseria, Yifei Lou, Guanghua Xiao and Yan Cao
2021, 15(1) : 27-40 doi: 10.3934/ipi.2020049 +[Abstract](545) +[HTML](259) +[PDF](2983.82KB)
Global convergence and geometric characterization of slow to fast weight evolution in neural network training for classifying linearly non-separable data
Ziang Long, Penghang Yin and Jack Xin
2021, 15(1) : 41-62 doi: 10.3934/ipi.2020077 +[Abstract](129) +[HTML](48) +[PDF](968.88KB)
Some worst-case datasets of deterministic first-order methods for solving binary logistic regression
Yuyuan Ouyang and Trevor Squires
2021, 15(1) : 63-77 doi: 10.3934/ipi.2020047 +[Abstract](404) +[HTML](213) +[PDF](335.47KB)
Stochastic greedy algorithms for multiple measurement vectors
Jing Qin, Shuang Li, Deanna Needell, Anna Ma, Rachel Grotheer, Chenxi Huang and Natalie Durgin
2021, 15(1) : 79-107 doi: 10.3934/ipi.2020066 +[Abstract](217) +[HTML](103) +[PDF](681.63KB)
Fast algorithms for robust principal component analysis with an upper bound on the rank
Ningyu Sha, Lei Shi and Ming Yan
2021, 15(1) : 109-128 doi: 10.3934/ipi.2020067 +[Abstract](230) +[HTML](109) +[PDF](2981.0KB)
Adversarial defense via the data-dependent activation, total variation minimization, and adversarial training
Bao Wang, Alex Lin, Penghang Yin, Wei Zhu, Andrea L. Bertozzi and Stanley J. Osher
2021, 15(1) : 129-145 doi: 10.3934/ipi.2020046 +[Abstract](453) +[HTML](230) +[PDF](2051.93KB)
A new initialization method based on normed statistical spaces in deep networks
Hongfei Yang, Xiaofeng Ding, Raymond Chan, Hui Hu, Yaxin Peng and Tieyong Zeng
2021, 15(1) : 147-158 doi: 10.3934/ipi.2020045 +[Abstract](408) +[HTML](229) +[PDF](286.77KB)
Fast non-convex low-rank matrix decomposition for separation of potential field data using minimal memory
Dan Zhu, Rosemary A. Renaut, Hongwei Li and Tianyou Liu
2021, 15(1) : 159-183 doi: 10.3934/ipi.2020076 +[Abstract](243) +[HTML](128) +[PDF](8790.84KB)
Image retinex based on the nonconvex TV-type regularization
Yuan Wang, Zhi-Feng Pang, Yuping Duan and Ke Chen
2020doi: 10.3934/ipi.2020050 +[Abstract](506) +[HTML](324) +[PDF](11956.02KB)
LANTERN: Learn analysis transform network for dynamic magnetic resonance imaging
Shanshan Wang, Yanxia Chen, Taohui Xiao, Lei Zhang, Xin Liu and Hairong Zheng
2020doi: 10.3934/ipi.2020051 +[Abstract](442) +[HTML](420) +[PDF](3273.78KB)
Automatic segmentation of the femur and tibia bones from X-ray images based on pure dilated residual U-Net
Weihao Shen, Wenbo Xu, Hongyang Zhang, Zexin Sun, Jianxiong Ma, Xinlong Ma, Shoujun Zhou, Shijie Guo and Yuanquan Wang
2020doi: 10.3934/ipi.2020057 +[Abstract](647) +[HTML](262) +[PDF](2807.14KB)
Leaf Peeling method for the wave equation on metric tree graphs
Sergei Avdonin and Yuanyuan Zhao
2020doi: 10.3934/ipi.2020060 +[Abstract](208) +[HTML](136) +[PDF](312.55KB)
Posterior contraction for empirical bayesian approach to inverse problems under non-diagonal assumption
Junxiong Jia, Jigen Peng and Jinghuai Gao
2020doi: 10.3934/ipi.2020061 +[Abstract](229) +[HTML](118) +[PDF](434.13KB)
Two new non-negativity preserving iterative regularization methods for ill-posed inverse problems
Ye Zhang and Bernd Hofmann
2020doi: 10.3934/ipi.2020062 +[Abstract](251) +[HTML](125) +[PDF](713.15KB)
Direct and inverse spectral problems for a star graph of Stieltjes strings damped at a pendant vertex
Lu Yang, Guangsheng Wei and Vyacheslav Pivovarchik
2020doi: 10.3934/ipi.2020063 +[Abstract](203) +[HTML](137) +[PDF](314.38KB)
Inverse scattering and stability for the biharmonic operator
Siamak RabieniaHaratbar
2020doi: 10.3934/ipi.2020064 +[Abstract](175) +[HTML](110) +[PDF](338.54KB)
Imaging junctions of waveguides
Laurent Bourgeois, Jean-François Fritsch and Arnaud Recoquillay
2020doi: 10.3934/ipi.2020065 +[Abstract](181) +[HTML](102) +[PDF](6538.97KB)
An adaptive total variational despeckling model based on gray level indicator frame
Yu Zhang, Songsong Li, Zhichang Guo and Boying Wu
2020doi: 10.3934/ipi.2020068 +[Abstract](193) +[HTML](141) +[PDF](6138.82KB)
RWRM: Residual Wasserstein regularization model for image restoration
Ruiqiang He, Xiangchu Feng, Xiaolong Zhu, Hua Huang and Bingzhe Wei
2020doi: 10.3934/ipi.2020069 +[Abstract](222) +[HTML](137) +[PDF](7831.84KB)
A new variational approach based on level-set function for convex hull problem with outliers
Lingfeng Li, Shousheng Luo, Xue-Cheng Tai and Jiang Yang
2020doi: 10.3934/ipi.2020070 +[Abstract](209) +[HTML](117) +[PDF](2740.5KB)
Bilinear constraint based ADMM for mixed Poisson-Gaussian noise removal
Jie Zhang, Yuping Duan, Yue Lu, Michael K. Ng and Huibin Chang
2020doi: 10.3934/ipi.2020071 +[Abstract](205) +[HTML](86) +[PDF](2287.64KB)
Duality between range and no-response tests and its application for inverse problems
Yi-Hsuan Lin, Gen Nakamura, Roland Potthast and Haibing Wang
2020doi: 10.3934/ipi.2020072 +[Abstract](208) +[HTML](66) +[PDF](376.94KB)
Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods
Wenbin Li and Jianliang Qian
2020doi: 10.3934/ipi.2020073 +[Abstract](185) +[HTML](80) +[PDF](1166.8KB)
Some application examples of minimization based formulations of inverse problems and their regularization
Kha Van Huynh and Barbara Kaltenbacher
2020doi: 10.3934/ipi.2020074 +[Abstract](194) +[HTML](142) +[PDF](529.49KB)
The interior transmission eigenvalue problem for elastic waves in media with obstacles
Fioralba Cakoni, Pu-Zhao Kow and Jenn-Nan Wang
2020doi: 10.3934/ipi.2020075 +[Abstract](211) +[HTML](86) +[PDF](419.39KB)
Tensor train rank minimization with nonlocal self-similarity for tensor completion
Meng Ding, Ting-Zhu Huang, Xi-Le Zhao, Michael K. Ng and Tian-Hui Ma
2020doi: 10.3934/ipi.2021001 +[Abstract](99) +[HTML](38) +[PDF](13497.32KB)
Inverse $N$-body scattering with the time-dependent hartree-fock approximation
Michiyuki Watanabe
2020doi: 10.3934/ipi.2021002 +[Abstract](75) +[HTML](36) +[PDF](390.32KB)
A nonlocal low rank model for poisson noise removal
Mingchao Zhao, You-Wei Wen, Michael Ng and Hongwei Li
2020doi: 10.3934/ipi.2021003 +[Abstract](136) +[HTML](93) +[PDF](11864.58KB)
The uniqueness of the inverse elastic wave scattering problem based on the mixed reciprocity relation
Jianli Xiang and Guozheng Yan
2020doi: 10.3934/ipi.2021004 +[Abstract](122) +[HTML](38) +[PDF](342.78KB)
Mathematical analysis of the acoustic imaging modality using bubbles as contrast agents at nearly resonating frequencies
Alexander Dabrowski, Ahcene Ghandriche and Mourad Sini
2020doi: 10.3934/ipi.2021005 +[Abstract](99) +[HTML](38) +[PDF](517.63KB)
A regularization operator for source identification for elliptic PDEs
Ole Løseth Elvetun and Bjørn Fredrik Nielsen
2020doi: 10.3934/ipi.2021006 +[Abstract](104) +[HTML](36) +[PDF](1301.19KB)
Fast dual minimization of the vectorial total variation norm and applications to color image processing
Xavier Bresson and Tony F. Chan
2008, 2(4) : 455-484 doi: 10.3934/ipi.2008.2.455 +[Abstract](4920) +[PDF](1915.3KB) Cited By(163)
The interior transmission problem
David Colton, Lassi Päivärinta and John Sylvester
2007, 1(1) : 13-28 doi: 10.3934/ipi.2007.1.13 +[Abstract](3482) +[PDF](204.8KB) Cited By(143)
Two-phase approach for deblurring images corrupted by impulse plus gaussian noise
Jian-Feng Cai, Raymond H. Chan and Mila Nikolova
2008, 2(2) : 187-204 doi: 10.3934/ipi.2008.2.187 +[Abstract](4060) +[PDF](922.2KB) Cited By(90)
On the existence of transmission eigenvalues
Andreas Kirsch
2009, 3(2) : 155-172 doi: 10.3934/ipi.2009.3.155 +[Abstract](3367) +[PDF](214.7KB) Cited By(85)
Regularized D-bar method for the inverse conductivity problem
Kim Knudsen, Matti Lassas, Jennifer L. Mueller and Samuli Siltanen
2009, 3(4) : 599-624 doi: 10.3934/ipi.2009.3.599 +[Abstract](3821) +[PDF](451.7KB) Cited By(84)
Iteratively solving linear inverse problems under general convex constraints
Ingrid Daubechies, Gerd Teschke and Luminita Vese
2007, 1(1) : 29-46 doi: 10.3934/ipi.2007.1.29 +[Abstract](3826) +[PDF](270.3KB) Cited By(76)
Augmented Lagrangian method for total variation restoration with non-quadratic fidelity
Chunlin Wu, Juyong Zhang and Xue-Cheng Tai
2011, 5(1) : 237-261 doi: 10.3934/ipi.2011.5.237 +[Abstract](5371) +[PDF](2454.5KB) Cited By(74)
Parallel matrix factorization for low-rank tensor completion
Yangyang Xu, Ruru Hao, Wotao Yin and Zhixun Su
2015, 9(2) : 601-624 doi: 10.3934/ipi.2015.9.601 +[Abstract](4184) +[PDF](839.8KB) Cited By(73)
Discretization-invariant Bayesian inversion and Besov space priors
Matti Lassas, Eero Saksman and Samuli Siltanen
2009, 3(1) : 87-122 doi: 10.3934/ipi.2009.3.87 +[Abstract](3456) +[PDF](441.9KB) Cited By(63)
On uniqueness in the inverse conductivity problem with local data
Victor Isakov
2007, 1(1) : 95-105 doi: 10.3934/ipi.2007.1.95 +[Abstract](3537) +[PDF](156.4KB) Cited By(63)
A Newton method for reconstructing non star-shaped domains in electrical impedance tomography
Helmut Harbrecht and Thorsten Hohage
2009, 3(2) : 353-371 doi: 10.3934/ipi.2009.3.353 +[Abstract](2344) +[PDF](902.3KB) PDF Downloads(4546)
Geometric mode decomposition
Siwei Yu, Jianwei Ma and Stanley Osher
2018, 12(4) : 831-852 doi: 10.3934/ipi.2018035 +[Abstract](5726) +[HTML](397) +[PDF](3108.34KB) PDF Downloads(372)
Poisson image denoising based on fractional-order total variation
Mujibur Rahman Chowdhury, Jun Zhang, Jing Qin and Yifei Lou
2020, 14(1) : 77-96 doi: 10.3934/ipi.2019064 +[Abstract](2989) +[HTML](408) +[PDF](1475.63KB) PDF Downloads(364)
Incorporating structural prior information and sparsity into EIT using parallel level sets
Ville Kolehmainen, Matthias J. Ehrhardt and Simon R. Arridge
2019, 13(2) : 285-307 doi: 10.3934/ipi.2019015 +[Abstract](4050) +[HTML](926) +[PDF](1075.82KB) PDF Downloads(336)
Nonlinear stability of the implicit-explicit methods for the Allen-Cahn equation
Xinlong Feng, Huailing Song, Tao Tang and Jiang Yang
2013, 7(3) : 679-695 doi: 10.3934/ipi.2013.7.679 +[Abstract](3136) +[PDF](866.5KB) PDF Downloads(323)
Nonlocal regularized CNN for image segmentation
Fan Jia, Xue-Cheng Tai and Jun Liu
2020, 14(5) : 891-911 doi: 10.3934/ipi.2020041 +[Abstract](1069) +[HTML](249) +[PDF](2876.37KB) PDF Downloads(313)
Time-invariant radon transform by generalized Fourier slice theorem
Ali Gholami and Mauricio D. Sacchi
2017, 11(3) : 501-519 doi: 10.3934/ipi.2017023 +[Abstract](4717) +[HTML](85) +[PDF](4112.8KB) PDF Downloads(300)
An inverse problem for the Sturm-Liouville pencil with arbitrary entire functions in the boundary condition
Chuan-Fu Yang, Natalia Pavlovna Bondarenko and Xiao-Chuan Xu
2020, 14(1) : 153-169 doi: 10.3934/ipi.2019068 +[Abstract](2318) +[HTML](175) +[PDF](340.84KB) PDF Downloads(257)
Nonlocal TV-Gaussian prior for Bayesian inverse problems with applications to limited CT reconstruction
Didi Lv, Qingping Zhou, Jae Kyu Choi, Jinglai Li and Xiaoqun Zhang
2020, 14(1) : 117-132 doi: 10.3934/ipi.2019066 +[Abstract](1859) +[HTML](398) +[PDF](2355.85KB) PDF Downloads(255)
Coordinate descent optimization for l1 minimization with application to compressed sensing; a greedy algorithm
Yingying Li and Stanley Osher
2009, 3(3) : 487-503 doi: 10.3934/ipi.2009.3.487 +[Abstract](3138) +[PDF](682.0KB) PDF Downloads(250)

2019  Impact Factor: 1.373

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