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Inverse Problems and Imaging includes 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, stochastic and statistical methods. The field of applications include 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.
IPI will have four issues published in 2015 in February, May, August and November.
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TOP 10 Most Read Articles in IPI, March 2015
1 
Wavelet inpainting by nonlocal total variation
Volume 4, Number 1, Pages: 191  210, 2010
Xiaoqun Zhang
and Tony F. Chan
Abstract
Full Text
Related Articles
Wavelet inpainting problem consists of filling in missed data in the wavelet domain. In [17], Chan, Shen, and Zhou proposed an efficient method to recover piecewise constant or smooth images by combining total variation regularization and wavelet representations. In this paper, we extend it to nonlocal total variation regularization in order to recover textures and local geometry structures simultaneously. Moreover, we apply an efficient algorithm framework for both local and nonlocal regularizers. Extensive
experimental results on a variety of loss scenarios and natural
images validate the performance of this approach.

2 
Correlation priors
Volume 5, Number 1, Pages: 167  184, 2011
Lassi Roininen,
Markku S. Lehtinen,
Sari Lasanen,
Mikko Orispää
and Markku Markkanen
Abstract
References
Full Text
Related Articles
We propose a new class of Gaussian priors, correlation priors. In contrast to some wellknown smoothness priors, they have stationary covariances. The correlation priors are given in a parametric form with two parameters: correlation power and correlation length. The first parameter is connected with our prior information on the variance of the unknown. The second parameter is our prior belief on how fast the correlation of the unknown approaches zero. Roughly speaking, the correlation length is the distance beyond which two points of the unknown may be considered independent.
The prior distribution is constructed to be essentially independent of the discretization so that the a posteriori distribution will be essentially independent of the discretization grid. The covariance of a discrete correlation prior may be formed by combining the Fisher information of a discrete white noise and differentorder difference priors. This is interpreted as a combination of virtual measurements of the unknown. Closedform expressions for the continuous limits are calculated. Also, boundary correction terms for correlation priors on finite intervals are given.
A numerical example, deconvolution with a Gaussian kernel and a correlation prior, is computed.

3 
Identification of soundsoft 3D obstacles from phaseless data
Volume 4, Number 1, Pages: 131  149, 2010
Olha Ivanyshyn
and Rainer Kress
Abstract
Full Text
Related Articles
The inverse problem for timeharmonic acoustic wave scattering to recover a soundsoft obstacle from a
given incident field and the far field pattern of the scattered field is considered. We split this problem into two
subproblems; first to reconstruct the shape from the modulus of the data and this is followed by
employing the full far field
pattern in a few measurement points to find the location of the obstacle.
We extend a nonlinear integral equation approach for shape reconstruction from the modulus of the far field
data [6] to the threedimensional case. It is known, see [13], that the location
of the obstacle cannot be reconstructed from only the modulus of the far field pattern since it is invariant under
translations. However, employing the underlying invariance relation
and using only few far field measurements in the backscattering direction we
propose a novel approach for the localization of the obstacle.
The efficient implementation of the method is described and the feasibility of the approach is illustrated by numerical
examples.

4 
A twolevel domain decomposition method for image restoration
Volume 4, Number 3, Pages: 523  545, 2010
Jing Xu,
XueCheng Tai
and LiLian Wang
Abstract
Full Text
Related Articles
Image restoration has drawn much attention in recent years and a
surge of research has been done on variational models and their
numerical studies. However, there remains an urgent need to
develop fast and robust methods for solving the minimization
problems and the underlying nonlinear PDEs to process images of
moderate to large size. This paper aims to propose a twolevel
domain decomposition method, which consists of an overlapping domain
decomposition technique and a coarse mesh correction, for directly
solving the total variational minimization problems. The iterative
algorithm leads to a system of small size and better conditioning
in each subspace, and is accelerated with a piecewise linear coarse
mesh correction. Various numerical experiments and comparisons
demonstrate that the proposed method is fast and robust particularly
for images of large size.

5 
Augmented Lagrangian method for total variation restoration with nonquadratic fidelity
Volume 5, Number 1, Pages: 237  261, 2011
Chunlin Wu,
Juyong Zhang
and XueCheng Tai
Abstract
References
Full Text
Related Articles
Recently augmented Lagrangian method has been successfully applied
to image restoration. We extend the method to total variation (TV)
restoration models with nonquadratic fidelities. We will first
introduce the method and present an iterative algorithm for TV
restoration with a quite general fidelity. In each iteration, three
subproblems need to be solved, two of which can be very efficiently
solved via Fast Fourier Transform (FFT) implementation or closed
form solution. In general the third subproblem need iterative
solvers. We then apply our method to TV restoration with $L^1$ and
KullbackLeibler (KL) fidelities, two common and important data
terms for deblurring images corrupted by impulsive noise and Poisson
noise, respectively. For these typical fidelities, we show that the
third subproblem also has closed form solution and thus can be
efficiently solved. In addition, convergence analysis of these
algorithms are given. Numerical experiments demonstrate the
efficiency of our method.

6 
Template matching via $l_1$ minimization and its application to hyperspectral data
Volume 5, Number 1, Pages: 19  35, 2011
Zhaohui Guo
and Stanley Osher
Abstract
References
Full Text
Related Articles
Detecting and identifying targets or objects that are present in
hyperspectral ground images are of great interest. Applications
include land and environmental monitoring, mining, military, civil
searchandrescue operations, and so on. We propose and analyze an
extremely simple and efficient idea for template matching based on
$l_1$ minimization. The designed algorithm can be applied in
hyperspectral classification and target detection. Synthetic image
data and real hyperspectral image (HSI) data are used to assess the
performance, with comparisons to other approaches, e.g. spectral
angle map (SAM), adaptive coherence estimator (ACE),
generalizedlikelihood ratio test (GLRT) and matched filter. We
demonstrate that this algorithm achieves excellent results with both
high speed and accuracy by using Bregman iteration.

7 
The interior transmission problem
Volume 1, Number 1, Pages: 13  28, 2007
David Colton,
Lassi Päivärinta
and John Sylvester
Abstract
Full Text
Related Articles
The interior transmission problem is a boundary value problem that plays a basic role in inverse scattering theory but unfortunately does not seem to be included in any existing theory in partial differential equations.This paper presents old and new results for the interior transmission problem ,in particular its relation to inverse scattering theory and new results on the spectral theory associated with this class of boundary value problems.

8 
Convex source support in halfplane
Volume 4, Number 3, Pages: 429  448, 2010
Lauri Harhanen
and Nuutti Hyvönen
Abstract
Full Text
Related Articles
This work extends the concept of convex source support
to the framework of inverse source problems for the Poisson equation in an
insulated upper halfplane. The convex source support is, in essence,
the smallest (nonempty) convex set that supports a source that produces
the measured (nontrivial) data on the horizontal axis. In particular, it belongs
to the convex hull of the support of any source that is compatible with the measurements.
We modify a previously introduced method for reconstructing the
convex source support in bounded domains to our unbounded setting.
The performance of the resulting numerical algorithm is analyzed both for the
inverse source problem and for electrical impedance tomography with single
pair of boundary current and potential as the measurement data.

9 
Remarks on the general
Funk transform and thermoacoustic tomography
Volume 4, Number 4, Pages: 693  702, 2010
Victor Palamodov
Abstract
References
Full Text
Related Articles
We discuss properties of a generalized MinkowskiFunk transform defined for
a family of hypersurfaces. We prove twoside estimates and show that the
range conditions can be written in terms of the reciprocal Funk transform.
Some applications to the spherical mean transform are considered.

10 
Localized potentials in electrical impedance tomography
Volume 2, Number 2, Pages: 251  269, 2008
Bastian Gebauer
Abstract
References
Full Text
Related Articles
In this work we study localized electric potentials that have an arbitrarily high energy on some given subset of a
domain and low energy on another. We show that such potentials exist for general $L^\infty_+$conductivities in
almost arbitrarily shaped subregions of a domain, as long as these regions are connected to the boundary and a unique continuation principle is satisfied. From this we deduce a simple, but new, theoretical identifiability result
for the famous Calderón problem with partial data. We also show how to construct such potentials numerically
and use a connection with the factorization method to derive a new noniterative algorithm for
the detection of inclusions in electrical impedance tomography.

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