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Call for Papers: Special Issue of IPI on “Helsinki Deblur Challenge 2021” (click to view details)
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 (IPI) 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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Preface
De-Xing Kong, Chunming Li, Xue-Cheng Tai and Jing Yuan
2021, 15(6) : Ⅰ-Ⅱ doi: 10.3934/ipi.2021070 +[Abstract](302) +[HTML](26) +[PDF](64.47KB)
Limited-angle CT reconstruction with generalized shrinkage operators as regularizers
Xiaojuan Deng, Xing Zhao, Mengfei Li and Hongwei Li
2021, 15(6) : 1287-1306 doi: 10.3934/ipi.2021019 +[Abstract](900) +[HTML](356) +[PDF](1601.74KB)
RWRM: Residual Wasserstein regularization model for image restoration
Ruiqiang He, Xiangchu Feng, Xiaolong Zhu, Hua Huang and Bingzhe Wei
2021, 15(6) : 1307-1332 doi: 10.3934/ipi.2020069 +[Abstract](1065) +[HTML](510) +[PDF](7835.33KB)
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
2021, 15(6) : 1333-1346 doi: 10.3934/ipi.2020057 +[Abstract](1941) +[HTML](856) +[PDF](2745.15KB)
Nonlocal latent low rank sparse representation for single image super resolution via self-similarity learning
Changming Song and Yun Wang
2021, 15(6) : 1347-1362 doi: 10.3934/ipi.2021017 +[Abstract](670) +[HTML](342) +[PDF](773.72KB)
LANTERN: Learn analysis transform network for dynamic magnetic resonance imaging
Shanshan Wang, Yanxia Chen, Taohui Xiao, Lei Zhang, Xin Liu and Hairong Zheng
2021, 15(6) : 1363-1379 doi: 10.3934/ipi.2020051 +[Abstract](1364) +[HTML](863) +[PDF](5013.13KB)
Image retinex based on the nonconvex TV-type regularization
Yuan Wang, Zhi-Feng Pang, Yuping Duan and Ke Chen
2021, 15(6) : 1381-1407 doi: 10.3934/ipi.2020050 +[Abstract](1652) +[HTML](762) +[PDF](11965.85KB)
Image fusion network for dual-modal restoration
Ying Zhang, Xuhua Ren, Bryan Alexander Clifford, Qian Wang and Xiaoqun Zhang
2021, 15(6) : 1409-1419 doi: 10.3934/ipi.2021067 +[Abstract](135) +[HTML](68) +[PDF](2897.95KB)
An adaptive total variational despeckling model based on gray level indicator frame
Yu Zhang, Songsong Li, Zhichang Guo and Boying Wu
2021, 15(6) : 1421-1450 doi: 10.3934/ipi.2020068 +[Abstract](913) +[HTML](524) +[PDF](6147.66KB)
A fast explicit diffusion algorithm of fractional order anisotropic diffusion for image denoising
Zhiguang Zhang, Qiang Liu and Tianling Gao
2021, 15(6) : 1451-1469 doi: 10.3934/ipi.2021018 +[Abstract](869) +[HTML](510) +[PDF](10243.11KB)
A stable non-iterative reconstruction algorithm for the acoustic inverse boundary value problem
Tianyu Yang and Yang Yang
2021doi: 10.3934/ipi.2021038 +[Abstract](618) +[HTML](274) +[PDF](4814.61KB)
Overcomplete representation in a hierarchical Bayesian framework
Monica Pragliola, Daniela Calvetti and Erkki Somersalo
2021doi: 10.3934/ipi.2021039 +[Abstract](510) +[HTML](237) +[PDF](5758.03KB)
Inverse problems for a half-order time-fractional diffusion equation in arbitrary dimension by Carleman estimates
Xinchi Huang and Atsushi Kawamoto
2021doi: 10.3934/ipi.2021040 +[Abstract](467) +[HTML](251) +[PDF](441.87KB)
A mathematical approach towards THz tomography for non-destructive imaging
Simon Hubmer, Alexander Ploier, Ronny Ramlau, Peter Fosodeder and Sandrine van Frank
2021doi: 10.3934/ipi.2021041 +[Abstract](536) +[HTML](246) +[PDF](14552.43KB)
On numerical aspects of parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging
Tram Thi Ngoc Nguyen and Anne Wald
2021doi: 10.3934/ipi.2021042 +[Abstract](524) +[HTML](297) +[PDF](3365.58KB)
A mathematical perspective on radar interferometry
Mikhail Gilman and Semyon Tsynkov
2021doi: 10.3934/ipi.2021043 +[Abstract](392) +[HTML](223) +[PDF](2621.95KB)
Smoothing Newton method for $ \ell^0 $-$ \ell^2 $ regularized linear inverse problem
Peili Li, Xiliang Lu and Yunhai Xiao
2021doi: 10.3934/ipi.2021044 +[Abstract](392) +[HTML](303) +[PDF](1758.82KB)
Learning to scan: A deep reinforcement learning approach for personalized scanning in CT imaging
Ziju Shen, Yufei Wang, Dufan Wu, Xu Yang and Bin Dong
2021doi: 10.3934/ipi.2021045 +[Abstract](449) +[HTML](209) +[PDF](3679.75KB)
Identification and stability of small-sized dislocations using a direct algorithm
Batoul Abdelaziz, Abdellatif El Badia and Ahmad El Hajj
2021doi: 10.3934/ipi.2021046 +[Abstract](338) +[HTML](187) +[PDF](596.72KB)
Partial inversion of the 2D attenuated $ X $-ray transform with data on an arc
Hiroshi Fujiwara, Kamran Sadiq and Alexandru Tamasan
2021doi: 10.3934/ipi.2021047 +[Abstract](439) +[HTML](196) +[PDF](989.31KB)
Refined stability estimates in electrical impedance tomography with multi-layer structure
Haigang Li, Jenn-Nan Wang and Ling Wang
2021doi: 10.3934/ipi.2021048 +[Abstract](402) +[HTML](216) +[PDF](471.43KB)
Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation
María Ángeles García-Ferrero, Angkana Rüland and Wiktoria Zatoń
2021doi: 10.3934/ipi.2021049 +[Abstract](424) +[HTML](186) +[PDF](486.62KB)
Variational source conditions for inverse Robin and flux problems by partial measurements
De-Han Chen, Daijun Jiang, Irwin Yousept and Jun Zou
2021doi: 10.3934/ipi.2021050 +[Abstract](403) +[HTML](210) +[PDF](638.51KB)
Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations
Ru-Yu Lai and Laurel Ohm
2021doi: 10.3934/ipi.2021051 +[Abstract](388) +[HTML](201) +[PDF](335.21KB)
Fourier method for reconstructing elastic body force from the coupled-wave field
Xianchao Wang, Jiaqi Zhu, Minghui Song and Wei Wu
2021doi: 10.3934/ipi.2021052 +[Abstract](416) +[HTML](227) +[PDF](1871.66KB)
PCA reduced Gaussian mixture models with applications in superresolution
Johannes Hertrich, Dang-Phuong-Lan Nguyen, Jean-Francois Aujol, Dominique Bernard, Yannick Berthoumieu, Abdellatif Saadaldin and Gabriele Steidl
2021doi: 10.3934/ipi.2021053 +[Abstract](357) +[HTML](135) +[PDF](1552.86KB)
A fuzzy edge detector driven telegraph total variation model for image despeckling
Sudeb Majee, Subit K. Jain, Rajendra K. Ray and Ananta K. Majee
2021doi: 10.3934/ipi.2021054 +[Abstract](337) +[HTML](168) +[PDF](6234.94KB)
An inverse source problem for the stochastic wave equation
Xiaoli Feng, Meixia Zhao, Peijun Li and Xu Wang
2021doi: 10.3934/ipi.2021055 +[Abstract](324) +[HTML](144) +[PDF](476.05KB)
Small defects reconstruction in waveguides from multifrequency one-side scattering data
Éric Bonnetier, Angèle Niclas, Laurent Seppecher and Grégory Vial
2021doi: 10.3934/ipi.2021056 +[Abstract](283) +[HTML](153) +[PDF](833.47KB)
Weighted area constraints-based breast lesion segmentation in ultrasound image analysis
Qianting Ma, Tieyong Zeng, Dexing Kong and Jianwei Zhang
2021doi: 10.3934/ipi.2021057 +[Abstract](259) +[HTML](104) +[PDF](3786.58KB)
Counterexamples to inverse problems for the wave equation
Tony Liimatainen and Lauri Oksanen
2021doi: 10.3934/ipi.2021058 +[Abstract](186) +[HTML](78) +[PDF](325.76KB)
Joint reconstruction and low-rank decomposition for dynamic inverse problems
Simon Arridge, Pascal Fernsel and Andreas Hauptmann
2021doi: 10.3934/ipi.2021059 +[Abstract](173) +[HTML](73) +[PDF](16060.57KB)
Generative imaging and image processing via generative encoder
Yong Zheng Ong and Haizhao Yang
2021doi: 10.3934/ipi.2021060 +[Abstract](182) +[HTML](121) +[PDF](2840.2KB)
A variational saturation-value model for image decomposition: Illumination and reflectance
Wei Wang and Caifei Li
2021doi: 10.3934/ipi.2021061 +[Abstract](131) +[HTML](74) +[PDF](34013.53KB)
Uniqueness and numerical reconstruction for inverse problems dealing with interval size search
Jone Apraiz, Jin Cheng, Anna Doubova, Enrique Fernández-Cara and Masahiro Yamamoto
2021doi: 10.3934/ipi.2021062 +[Abstract](158) +[HTML](63) +[PDF](2234.7KB)
On new surface-localized transmission eigenmodes
Youjun Deng, Yan Jiang, Hongyu Liu and Kai Zhang
2021doi: 10.3934/ipi.2021063 +[Abstract](140) +[HTML](68) +[PDF](491.58KB)
An inverse problem for a fractional diffusion equation with fractional power type nonlinearities
Li Li
2021doi: 10.3934/ipi.2021064 +[Abstract](135) +[HTML](70) +[PDF](369.24KB)
Nonconvex regularization for blurred images with Cauchy noise
Xiao Ai, Guoxi Ni and Tieyong Zeng
2021doi: 10.3934/ipi.2021065 +[Abstract](174) +[HTML](65) +[PDF](1969.69KB)
Automated filtering in the nonlinear Fourier domain of systematic artifacts in 2D electrical impedance tomography
Melody Alsaker, Benjamin Bladow, Scott E. Campbell and Emma M. Kar
2021doi: 10.3934/ipi.2021066 +[Abstract](157) +[HTML](105) +[PDF](11539.06KB)
Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data
Michael V. Klibanov, Thuy T. Le, Loc H. Nguyen, Anders Sullivan and Lam Nguyen
2021doi: 10.3934/ipi.2021068 +[Abstract](138) +[HTML](53) +[PDF](1997.13KB)
The interior inverse scattering problem for a two-layered cavity using the Bayesian method
Yunwen Yin, Weishi Yin, Pinchao Meng and Hongyu Liu
2021doi: 10.3934/ipi.2021069 +[Abstract](110) +[HTML](59) +[PDF](868.47KB)
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](6270) +[PDF](1915.3KB) Cited By(170)
The interior transmission problem
David Colton, Lassi Päivärinta and John Sylvester
2007, 1(1) : 13-28 doi: 10.3934/ipi.2007.1.13 +[Abstract](4533) +[PDF](204.8KB) Cited By(145)
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](5179) +[PDF](922.2KB) Cited By(96)
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](4751) +[PDF](451.7KB) Cited By(89)
On the existence of transmission eigenvalues
Andreas Kirsch
2009, 3(2) : 155-172 doi: 10.3934/ipi.2009.3.155 +[Abstract](4341) +[PDF](214.7KB) Cited By(86)
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](5875) +[PDF](839.8KB) Cited By(84)
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](6559) +[PDF](2454.5KB) Cited By(76)
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](4685) +[PDF](270.3KB) Cited By(76)
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](4458) +[PDF](441.9KB) Cited By(66)
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](4504) +[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](3192) +[PDF](902.3KB) PDF Downloads(4573)
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](2062) +[HTML](261) +[PDF](2876.37KB) PDF Downloads(788)
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](4192) +[PDF](682.0KB) PDF Downloads(714)
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](4186) +[HTML](420) +[PDF](1475.63KB) PDF Downloads(660)
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
2021, 15(6) : 1333-1346 doi: 10.3934/ipi.2020057 +[Abstract](1941) +[HTML](856) +[PDF](2745.15KB) PDF Downloads(644)
Geometric mode decomposition
Siwei Yu, Jianwei Ma and Stanley Osher
2018, 12(4) : 831-852 doi: 10.3934/ipi.2018035 +[Abstract](7095) +[HTML](417) +[PDF](3108.34KB) PDF Downloads(625)
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](5986) +[HTML](105) +[PDF](4112.8KB) PDF Downloads(612)
Two-dimensional seismic data reconstruction using patch tensor completion
Qun Liu, Lihua Fu, Meng Zhang and Wanjuan Zhang
2020, 14(6) : 985-1000 doi: 10.3934/ipi.2020052 +[Abstract](1505) +[HTML](251) +[PDF](5409.15KB) PDF Downloads(517)
Iterative choice of the optimal regularization parameter in TV image restoration
Alina Toma, Bruno Sixou and Françoise Peyrin
2015, 9(4) : 1171-1191 doi: 10.3934/ipi.2015.9.1171 +[Abstract](3315) +[PDF](2108.1KB) PDF Downloads(492)
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](5164) +[HTML](1331) +[PDF](1075.82KB) PDF Downloads(487)

2020 Impact Factor: 1.639
5 Year Impact Factor: 1.720
2020 CiteScore: 2.6

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