1
|
Takalo J, Timonen J, Sampo J, Rantala M, Siltanen S, Lassas M. Using the fibre structure of paper to determine authenticity of the documents: Analysis of transmitted light images of stamps and banknotes. Forensic Sci Int 2014; 244:252-8. [DOI: 10.1016/j.forsciint.2014.09.002] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2014] [Revised: 08/28/2014] [Accepted: 09/02/2014] [Indexed: 11/25/2022]
|
2
|
|
3
|
Kolehmainen V, Lassas M, Ola P, Siltanen S. Recovering boundary shape and conductivity in electrical impedance tomography. ACTA ACUST UNITED AC 2013. [DOI: 10.3934/ipi.2013.7.217] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
|
4
|
Greenleaf A, Kurylev Y, Lassas M, Uhlmann G. Cloaking a sensor via transformation optics. Phys Rev E Stat Nonlin Soft Matter Phys 2011; 83:016603. [PMID: 21405787 DOI: 10.1103/physreve.83.016603] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2009] [Revised: 10/31/2010] [Indexed: 05/30/2023]
Abstract
Ideal transformation optics cloaking at positive frequency, besides rendering the cloaked region invisible to detection by scattering of incident waves, also shields the region from those same waves. In contrast, we demonstrate that approximate cloaking permits a strong coupling between the cloaked and uncloaked regions; careful choice of parameters allows this coupling to be amplified, leading to effective cloaks with degraded shielding. The sensor modes we describe are close to but distinct from interior resonances, which destroy cloaking. As one application, we describe how to use transformation optics to hide sensors in the cloaked region and yet enable the sensors to efficiently measure incident waves on the exterior of the cloak, an effect similar to the plasmon-based approach of Alù and Engheta.
Collapse
Affiliation(s)
- Allan Greenleaf
- Department of Mathematics, University of Rochester, Rochester, New York 14627, USA
| | | | | | | |
Collapse
|
5
|
Hyvönen N, Kalke M, Lassas M, Setälä H, Siltanen S. Three-dimensional dental X-ray imaging by combination of panoramic and projection data. ACTA ACUST UNITED AC 2010. [DOI: 10.3934/ipi.2010.4.257] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
|
6
|
|
7
|
|
8
|
Greenleaf A, Kurylev Y, Lassas M, Uhlmann G. Approximate quantum cloaking and almost-trapped states. Phys Rev Lett 2008; 101:220404. [PMID: 19113466 DOI: 10.1103/physrevlett.101.220404] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2008] [Revised: 09/29/2008] [Indexed: 05/27/2023]
Abstract
We describe potentials which act as approximate cloaks for matter waves. These potentials are derived from ideal cloaks for the conductivity and Helmholtz equations. At most energies E, if a potential is surrounded by an approximate cloak, then it becomes almost undetectable and unaltered by matter waves originating externally to the cloak. For certain E, however, the approximate cloaks are resonant, supporting wave functions almost trapped inside the cloaked region and negligible outside. Applications include dc or magnetically tunable ion traps and beam switches.
Collapse
Affiliation(s)
- Allan Greenleaf
- Department of Mathematics, University of Rochester, Rochester, New York 14627, USA
| | | | | | | |
Collapse
|
9
|
Kolehmainen V, Lassas M, Ola P. Electrical impedance tomography problem with inaccurately known boundary and contact impedances. IEEE Trans Med Imaging 2008; 27:1404-1414. [PMID: 18815092 DOI: 10.1109/tmi.2008.920600] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
In electrical impedance tomography (EIT) electric currents are injected into a body with unknown electromagnetic properties through a set of contact electrodes at the boundary of the body. The resulting voltages are measured on the same electrodes and the objective is to reconstruct the unknown conductivity function inside the body based on these data. All the traditional approaches to the reconstruction problem assume that the boundary of the body and the electrode-skin contact impedances are known a priori. However, in clinical experiments one usually lacks the exact knowledge of the boundary and contact impedances, and therefore, approximate model domain and contact impedances have to be used in the image reconstruction. However, it has been noticed that even small errors in the shape of the computation domain or contact impedances can cause large systematic artefacts in the reconstructed images, leading to loss of diagnostically relevant information. In a recent paper (Kolehmainen , 2006), we showed how in the 2-D case the errors induced by the inaccurately known boundary can be eliminated as part of the image reconstruction and introduced a novel method for finding a deformed image of the original isotropic conductivity using the theory of TeichmUller mappings. In this paper, the theory and reconstruction method are extended to include the estimation of unknown contact impedances. The method is implemented numerically and tested with experimental EIT data. The results show that the systematic errors caused by inaccurately known boundary and contact impedances can efficiently be eliminated by the reconstruction method.
Collapse
Affiliation(s)
- Ville Kolehmainen
- Department of Applied Physics, University of Kuopio, FIN-70211 Kuopio, Finland
| | | | | |
Collapse
|
10
|
Knudsen K, Lassas M, Mueller J, Siltanen S. Reconstructions of piecewise constant conductivities by the D-bar method for electrical impedance tomography. ACTA ACUST UNITED AC 2008. [DOI: 10.1088/1742-6596/124/1/012029] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
11
|
Greenleaf A, Kurylev Y, Lassas M, Uhlmann G. Electromagnetic wormholes and virtual magnetic monopoles from metamaterials. Phys Rev Lett 2007; 99:183901. [PMID: 17995408 DOI: 10.1103/physrevlett.99.183901] [Citation(s) in RCA: 64] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2007] [Indexed: 05/25/2023]
Abstract
We describe new configurations of electromagnetic (EM) material parameters, the electric permittivity epsilon and magnetic permeability micro, which allow one to construct devices that function as invisible tunnels. These allow EM wave propagation between the regions at the two ends of a tunnel, but the tunnels themselves and the regions they enclose are not detectable to lateral EM observations. Such devices act as wormholes with respect to Maxwell's equations and effectively change the topology of space vis-à-vis EM wave propagation. We suggest several applications, including devices behaving as virtual magnetic monopoles, invisible cables, and scopes for MRI-assisted surgery.
Collapse
Affiliation(s)
- Allan Greenleaf
- Department Mathematics University of Rochester, Rochester, New York 14627, USA
| | | | | | | |
Collapse
|
12
|
Abstract
We analyze the effectiveness of cloaking an infinite cylinder from observations by electromagnetic waves in three dimensions. We show that, as truncated approximations of the ideal permittivity and permeability material parameters tend towards the singular ideal cloaking values, the D and B fields blow up near the cloaking surface. Since the metamaterials used to implement cloaking are based on effective medium theory, the resulting large variation in D and B poses a challenge to the suitability of the field-averaged characterization of epsilon and mu. We also consider cloaking with and without the SHS (soft-and-hard surface) lining. We demonstrate numerically that cloaking is significantly improved by the SHS lining, with both the far field of the scattered wave significantly reduced and the blow up of D and B prevented.
Collapse
|
13
|
Rantala M, Vänskä S, Järvenpää S, Kalke M, Lassas M, Moberg J, Siltanen S. Wavelet-based reconstruction for limited-angle X-ray tomography. IEEE Trans Med Imaging 2006; 25:210-7. [PMID: 16468455 DOI: 10.1109/tmi.2005.862206] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
The aim of X-ray tomography is to reconstruct an unknown physical body from a collection of projection images. When the projection images are only available from a limited angle of view, the reconstruction problem is a severely ill-posed inverse problem. Statistical inversion allows stable solution of the limited-angle tomography problem by complementing the measurement data by a priori information. In this work, the unknown attenuation distribution inside the body is represented as a wavelet expansion, and a Besov space prior distribution together with positivity constraint is used. The wavelet expansion is thresholded before reconstruction to reduce the dimension of the computational problem. Feasibility of the method is demonstrated by numerical examples using in vitro data from mammography and dental radiology.
Collapse
|
14
|
Kolehmainen V, Vanne A, Siltanen S, Järvenpää S, Kaipio JP, Lassas M, Kalke M. Parallelized Bayesian inversion for three-dimensional dental X-ray imaging. IEEE Trans Med Imaging 2006; 25:218-28. [PMID: 16468456 DOI: 10.1109/tmi.2005.862662] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because of high radiation dose, low-resolution or the cost of the CT scanner equipment. In this paper, we consider a novel type of 3-D imaging modality for dental radiology. We consider situations in which projection images of the teeth are taken from a few sparsely distributed projection directions using the dentist's regular (digital) X-ray equipment and the 3-D X-ray attenuation function is reconstructed. A complication in these experiments is that the reconstruction of the 3-D structure based on a few projection images becomes an ill-posed inverse problem. Bayesian inversion is a well suited framework for reconstruction from such incomplete data. In Bayesian inversion, the ill-posed reconstruction problem is formulated in a well-posed probabilistic form in which a priori information is used to compensate for the incomplete information of the projection data. In this paper we propose a Bayesian method for 3-D reconstruction in dental radiology. The method is partially based on Kolehmainen et al. 2003. The prior model for dental structures consist of a weighted l1 and total variation (TV)-prior together with the positivity prior. The inverse problem is stated as finding the maximum a posteriori (MAP) estimate. To make the 3-D reconstruction computationally feasible, a parallelized version of an optimization algorithm is implemented for a Beowulf cluster computer. The method is tested with projection data from dental specimens and patient data. Tomosynthetic reconstructions are given as reference for the proposed method.
Collapse
|
15
|
Kolehmainen V, Siltanen S, Järvenpää S, Kaipio JP, Koistinen P, Lassas M, Pirttilä J, Somersalo E. Statistical inversion for medical x-ray tomography with few radiographs: II. Application to dental radiology. Phys Med Biol 2003; 48:1465-90. [PMID: 12812458 DOI: 10.1088/0031-9155/48/10/315] [Citation(s) in RCA: 65] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Abstract
Diagnostic and operational tasks in dental radiology often require three-dimensional information that is difficult or impossible to see in a projection image. A CT-scan provides the dentist with comprehensive three-dimensional data. However, often CT-scan is impractical and, instead, only a few projection radiographs with sparsely distributed projection directions are available. Statistical (Bayesian) inversion is well-suited approach for reconstruction from such incomplete data. In statistical inversion, a priori information is used to compensate for the incomplete information of the data. The inverse problem is recast in the form of statistical inference from the posterior probability distribution that is based on statistical models of the projection data and the a priori information of the tissue. In this paper, a statistical model for three-dimensional imaging of dentomaxillofacial structures is proposed. Optimization and MCMC algorithms are implemented for the computation of posterior statistics. Results are given with in vitro projection data that were taken with a commercial intraoral x-ray sensor. Examples include limited-angle tomography and full-angle tomography with sparse projection data. Reconstructions with traditional tomographic reconstruction methods are given as reference for the assessment of the estimates that are based on the statistical model.
Collapse
Affiliation(s)
- V Kolehmainen
- Department of Applied Physics, University of Kuopio, PO Box 1627, FIN-70211 Kuopio, Finland.
| | | | | | | | | | | | | | | |
Collapse
|
16
|
Siltanen S, Kolehmainen V, Järvenpää S, Kaipio JP, Koistinen P, Lassas M, Pirttilä J, Somersalo E. Statistical inversion for medical x-ray tomography with few radiographs: I. General theory. Phys Med Biol 2003; 48:1437-63. [PMID: 12812457 DOI: 10.1088/0031-9155/48/10/314] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
In x-ray tomography, the structure of a three-dimensional body is reconstructed from a collection of projection images of the body. Medical CT imaging does this using an extensive set of projections from all around the body. However, in many practical imaging situations only a small number of truncated projections are available from a limited angle of view. Three-dimensional imaging using such data is complicated for two reasons: (i) typically, sparse projection data do not contain sufficient information to completely describe the 3D body, and (ii) traditional CT reconstruction algorithms, such as filtered backprojection, do not work well when applied to few irregularly spaced projections. Concerning (i), existing results about the information content of sparse projection data are reviewed and discussed. Concerning (ii), it is shown how Bayesian inversion methods can be used to incorporate a priori information into the reconstruction method, leading to improved image quality over traditional methods. Based on the discussion, a low-dose three-dimensional x-ray imaging modality is described.
Collapse
Affiliation(s)
- S Siltanen
- Instrumentarium Corp. Imaging Division, PO Box 20, FIN-04301 Tuusula, Finland
| | | | | | | | | | | | | | | |
Collapse
|
17
|
Abstract
We construct anisotropic conductivities in dimension 3 that give rise to the same voltage and current measurements at the boundary of a body as a homogeneous isotropic conductivity. These conductivities are non-zero, but degenerate close to a surface inside the body.
Collapse
Affiliation(s)
- Allan Greenleaf
- Department of Mathematics, University of Rochester, Rochester, NY 14618, USA
| | | | | |
Collapse
|