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 1930-8337

eISSN:
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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.

This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 6 issues a year in February, April, June, August, October and December.
  • Publishes online only.
  • Indexed in Science Citation Index, ISI Alerting Services, CompuMath Citation Index, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), INSPEC, Mathematical Reviews, MathSciNet, PASCAL/CNRS, Scopus, Web of Science and Zentralblatt MATH.
  • Archived in Portico and CLOCKSS.
  • IPI is a publication of the American Institute of Mathematical Sciences. All rights reserved.

Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.

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A variational model with fractional-order regularization term arising in registration of diffusion tensor image
Huan Han
2018, 12(6) : 1263-1291 doi: 10.3934/ipi.2018053 +[Abstract](68) +[HTML](37) +[PDF](742.1KB)
Abstract:

In this paper, a new variational model with fractional-order regularization term arising in registration of diffusion tensor image(DTI) is presented. Moreover, the existence of its solution is proved to ensure that there is a regular solution for this model. Furthermore, three numerical tests are also performed to show the effectiveness of this model.

Reconstruction of the coefficients of a star graph from observations of its vertices
Amin Boumenir and Vu Kim Tuan
2018, 12(6) : 1293-1308 doi: 10.3934/ipi.2018054 +[Abstract](53) +[HTML](33) +[PDF](369.33KB)
Abstract:

Consider a three-edge star graph, made up of unknown Sturm-Liouville operators on each edge. By using the heat propagation through the graph and measuring the heat transfer occurring at its vertices, we show that we can extract enough spectral data to reconstruct the three Sturm-Liouville operators by using the Gelfand-Levitan theory. Furthermore this reconstruction is achieved by a single measurement provided we use a special initial condition.

Stability estimates for a magnetic Schrödinger operator with partial data
Leyter Potenciano-Machado and Alberto Ruiz
2018, 12(6) : 1309-1342 doi: 10.3934/ipi.2018055 +[Abstract](51) +[HTML](28) +[PDF](553.67KB)
Abstract:

In this paper we study local stability estimates for a magnetic Schrödinger operator with partial data on an open bounded set in dimension \begin{document}$ n≥3$\end{document}. This is the corresponding stability estimates for the identifiability result obtained by Bukhgeim and Uhlmann [2] in the presence of a magnetic field and when the measurements for the Dirichlet-Neumann map are taken on a neighborhood of the illuminated region of the boundary for functions supported on a neighborhood of the shadow region. We obtain log log-estimates for the magnetic fields and log log log-estimates for the electric potentials.

Simultaneous reconstruction and segmentation with the Mumford-Shah functional for electron tomography
Li Shen, Eric Todd Quinto, Shiqiang Wang and Ming Jiang
2018, 12(6) : 1343-1364 doi: 10.3934/ipi.2018056 +[Abstract](70) +[HTML](32) +[PDF](2889.55KB)
Abstract:

Electron micrography (EM) is a detection method for determining the structure of macromolecular complexes and biological specimens. However, some restrictions in the EM system, including poor signal-to-noise, limited range of tilt angles, only a sub-region subject to electron exposure and unintentional movements of the specimen, make the reconstruction procedure severely ill-posed. Because of these limitations, there may be severe artifacts in reconstructed images. In this paper, we first design an algorithm that can quickly calculate the radiological paths. Then we combine an iterative reconstruction algorithm using the Mumford-Shah model with an artifact reduction strategy. The combined method can not only regularize the ill-posedness and provide the reconstruction and segmentation simultaneously but also smooth additional artifacts due to the limited data. Also we improved the algorithm used for the calculation of radiological paths to accelerate the reconstruction. The proposed algorithm was translated into OpenCL programs and kernel functions to asynchronously and in parallel update the reconstructed image along rays by GPUs. We tested the method on both simulated and real EM data. The results show that our artifact reduced Mumford-Shah algorithm can reduce the noise and artifacts while preserving and enhancing the edges in the reconstructed image.

Lens rigidity with partial data in the presence of a magnetic field
Hanming Zhou
2018, 12(6) : 1365-1387 doi: 10.3934/ipi.2018057 +[Abstract](49) +[HTML](30) +[PDF](545.01KB)
Abstract:

In this paper we consider the lens rigidity problem with partial data for conformal metrics in the presence of a magnetic field on a compact manifold of dimension \begin{document}$≥ 3$\end{document} with boundary. We show that one can uniquely determine the conformal factor and the magnetic field near a strictly convex (with respect to the magnetic geodesics) boundary point where the lens data is accessible. We also prove a boundary rigidity result with partial data assuming the lengths of magnetic geodesics joining boundary points near a strictly convex boundary point are known. The local lens rigidity result also leads to a global rigidity result under some strictly convex foliation condition. A discussion of a weaker version of the lens rigidity problem with partial data for general smooth curves is given at the end of the paper.

Local block operators and TV regularization based image inpainting
Wei Wan, Haiyang Huang and Jun Liu
2018, 12(6) : 1389-1410 doi: 10.3934/ipi.2018058 +[Abstract](59) +[HTML](48) +[PDF](2981.83KB)
Abstract:

In this paper, we propose a novel image blocks based inpainting model using group sparsity and TV regularization. The block matching method is employed to collect similar image blocks which can be formed as sparse image groups. By reducing the redundant information in these groups, we can well restore textures missing in the inpainting areas. We built a variational framework based on a local SVD operator for block matching and group sparsity. In addition, TV regularization is naturally integrated in the model to reduce artificial effects which are caused by image blocks stacking in the block matching method. Besides, enforcing the sparsity of the representation, the SVD operators in our method are iteratively updated and play the role of dictionary learning. Thus it can greatly improve the quality of the restoration. Moreover, we mathematically show the existence of a minimizer for the proposed inpainting model. Convergence results of the proposed algorithm are also given in the paper. Numerical experiments demonstrate that the proposed model outperforms many benchmark methods such as BM3D based image inpainting.

Inverse source problems in electrodynamics
Guanghui Hu, Peijun Li, Xiaodong Liu and Yue Zhao
2018, 12(6) : 1411-1428 doi: 10.3934/ipi.2018059 +[Abstract](57) +[HTML](34) +[PDF](542.49KB)
Abstract:

This paper concerns inverse source problems for the time-dependent Maxwell equations. The electric current density is assumed to be the product of a spatial function and a temporal function. We prove uniqueness and stability in determining the spatial or temporal function from the electric field, which is measured on a sphere or at a point over a finite time interval.

Tomographic reconstruction methods for decomposing directional components
Rasmus Dalgas Kongskov and Yiqiu Dong
2018, 12(6) : 1429-1442 doi: 10.3934/ipi.2018060 +[Abstract](54) +[HTML](33) +[PDF](1782.64KB)
Abstract:

X-ray computed tomography technique has been used in many different practical applications. Often after reconstruction we need segment or decompose objects into different components. In this paper, we propose two new reconstruction methods that can decompose objects at the same time. By incorporating direction information, the proposed methods can decompose objects into various directional components. Furthermore, we propose an algorithm to obtain the direction information of the object directly from its CT measurements. We demonstrate the proposed methods on simulated and real samples to show their practical applicability. The numerical results show the differences between the two methods and effectiveness as dealing with fibre-crack decomposition problems.

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](1295) +[PDF](1915.3KB) Cited By(111)
The interior transmission problem
David Colton, Lassi Päivärinta and John Sylvester
2007, 1(1) : 13-28 doi: 10.3934/ipi.2007.1.13 +[Abstract](762) +[PDF](204.8KB) Cited By(106)
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](1140) +[PDF](922.2KB) Cited By(69)
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](950) +[PDF](270.3KB) Cited By(59)
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](833) +[PDF](451.7KB) Cited By(53)
On the existence of transmission eigenvalues
Andreas Kirsch
2009, 3(2) : 155-172 doi: 10.3934/ipi.2009.3.155 +[Abstract](873) +[PDF](214.7KB) Cited By(51)
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](1354) +[PDF](2454.5KB) Cited By(48)
Non-local regularization of inverse problems
Gabriel Peyré, Sébastien Bougleux and Laurent Cohen
2011, 5(2) : 511-530 doi: 10.3934/ipi.2011.5.511 +[Abstract](1042) +[PDF](1841.8KB) Cited By(42)
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](1012) +[PDF](156.4KB) Cited By(41)
Photo-acoustic inversion in convex domains
Frank Natterer
2012, 6(2) : 315-320 doi: 10.3934/ipi.2012.6.315 +[Abstract](657) +[PDF](238.1KB) Cited By(39)
\begin{document} $\ell_{0}$ \end{document} and \begin{document} $\ell_{2}$ \end{document} regularizations for limited-angle CT reconstruction" >Existence and convergence analysis of $\ell_{0}$ and $\ell_{2}$ regularizations for limited-angle CT reconstruction
Chengxiang Wang, Li Zeng, Wei Yu and Liwei Xu
2018, 12(3) : 545-572 doi: 10.3934/ipi.2018024 +[Abstract](770) +[HTML](263) +[PDF](955.55KB) PDF Downloads(108)
Backward problem for a time-space fractional diffusion equation
Junxiong Jia, Jigen Peng, Jinghuai Gao and Yujiao Li
2018, 12(3) : 773-799 doi: 10.3934/ipi.2018033 +[Abstract](997) +[HTML](272) +[PDF](659.55KB) PDF Downloads(100)
Recovering a large number of diffusion constants in a parabolic equation from energy measurements
Gianluca Mola
2018, 12(3) : 527-543 doi: 10.3934/ipi.2018023 +[Abstract](558) +[HTML](179) +[PDF](426.47KB) PDF Downloads(97)
Geometric mode decomposition
Siwei Yu, Jianwei Ma and Stanley Osher
2018, 12(4) : 831-852 doi: 10.3934/ipi.2018035 +[Abstract](608) +[HTML](228) +[PDF](3108.34KB) PDF Downloads(95)
A scaled gradient method for digital tomographic image reconstruction
Jianjun Zhang, Yunyi Hu and James G. Nagy
2018, 12(1) : 239-259 doi: 10.3934/ipi.2018010 +[Abstract](921) +[HTML](365) +[PDF](779.26KB) PDF Downloads(95)
Risk estimators for choosing regularization parameters in ill-posed problems - properties and limitations
Felix Lucka, Katharina Proksch, Christoph Brune, Nicolai Bissantz, Martin Burger, Holger Dette and Frank Wübbeling
2018, 12(5) : 1121-1155 doi: 10.3934/ipi.2018047 +[Abstract](420) +[HTML](274) +[PDF](2945.43KB) PDF Downloads(88)
Using generalized cross validation to select regularization parameter for total variation regularization problems
You-Wei Wen and Raymond Honfu Chan
2018, 12(5) : 1103-1120 doi: 10.3934/ipi.2018046 +[Abstract](448) +[HTML](135) +[PDF](1676.42KB) PDF Downloads(88)
Fluid image registration using a finite volume scheme of the incompressible Navier Stokes equation
Mohamed Alahyane, Abdelilah Hakim, Amine Laghrib and Said Raghay
2018, 12(5) : 1055-1081 doi: 10.3934/ipi.2018044 +[Abstract](306) +[HTML](213) +[PDF](1905.73KB) PDF Downloads(81)
SAR correlation imaging and anisotropic scattering
Kaitlyn (Voccola) Muller
2018, 12(3) : 697-731 doi: 10.3934/ipi.2018030 +[Abstract](625) +[HTML](223) +[PDF](2287.45KB) PDF Downloads(78)
A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data
Michael V. Klibanov, Dinh-Liem Nguyen, Loc H. Nguyen and Hui Liu
2018, 12(2) : 493-523 doi: 10.3934/ipi.2018021 +[Abstract](685) +[HTML](238) +[PDF](1037.64KB) PDF Downloads(73)

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