We present a review of methods for the forward and inverse problems in optical tomography. We limit ourselves to the highly scattering case found in applications in medical imaging, and to the problem of absorption and scattering reconstruction. We discuss the derivation of the diffusion approximation and other simplifications of the full transport problem. We…
Inverse Problems Template
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About the Inverse Problems format
Inverse Problems is a peer-reviewed journal published by IOP Publishing, covering Numerical methods in inverse problems, Microwave Imaging and Scattering Analysis, Advanced Mathematical Modeling in Engineering. Over its lifetime it has published 5,409 papers, which have received 178,328 citations.
| Publisher | IOP Publishing |
|---|---|
| Reference style | Numbered (IOP) Numbered — [1], [2] in the text [1] Smith A, Jones B and Lee C 2023 A representative article title Inverse Problems 12 45–58
Formats any DOI in Inverse Problems style. No sign-up. |
| Publishes research in | Numerical methods in inverse problems Microwave Imaging and Scattering Analysis Advanced Mathematical Modeling in Engineering Sparse and Compressive Sensing Techniques Electrical and Bioimpedance Tomography |
| ISSN | 0266-5611 |
| Citation impact (2-yr) | 1.92 |
| h-index | 163 |
| i10-index | 3,188 |
| Top institutions publishing here | Centre National de la Recherche Scientifique |
| Journal website | iopscience.org |
| You get | A submission-ready PDF and the editable LaTeX source — ready to submit. |
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Most-cited papers in Inverse Problems
We consider the problem of reconstructing a sparse signal x^0\\in{\\bb R}^n from a limited number of linear measurements. Given m randomly selected samples of Ux0, where U is an orthonormal matrix, we show that ell1 minimization recovers x0 exactly when the number of measurements exceeds \n \nm\\geq \\mathrm{const}^{\\vphantom{\\frac12}}_{\\vphantom{\\frac12}} \\cdot\\mu^2(U)\\cdot S\\cdot\\log n, \n \nwhere S is the number of nonzero…
Synthetic aperture radar (SAR) is a coherent active microwave imaging method. In remote sensing it is used for mapping the scattering properties of the Earth's surface in the respective wavelength domain. Many physical and geometric parameters of the imaged scene contribute to the grey value of a SAR image pixel. Scene inversion suffers from this…
Let T be a (possibly nonlinear) continuous operator on Hilbert space . If, for some starting vector x, the orbit sequence {Tkx,k = 0,1,...} converges, then the limit z is a fixed point of T; that is, Tz = z. An operator N on a Hilbert space is nonexpansive (ne) if, for each x and…
Let C and Q be nonempty closed convex sets in RN and RM, respectively, and A an M by N real matrix. The split feasibility problem (SFP) is to find x ∊ C with Ax ∊ Q, if such x exist. An iterative method for solving the SFP, called the CQ algorithm, has the following…