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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 2014 in February, May, August and November. 
TOP 10 Most Read Articles in IPI, September 2014
1 
Coordinate descent optimization for l^{1} minimization with application to compressed sensing; a greedy algorithm
Volume 3, Number 3, Pages: 487  503, 2009
Yingying Li
and Stanley Osher
Abstract
Full Text
Related Articles
We propose a fast algorithm for solving the Basis Pursuit problem, min_{u}
$\{u_1\: \Au=f\}$, which has application to compressed sensing.
We design an efficient method for solving the related unconstrained problem min_{u} $E(u) = u_1 + \lambda \Auf\^2_2$ based on a greedy coordinate descent
method. We claim that in combination with a Bregman iterative method, our
algorithm will achieve a solution with speed and accuracy competitive with some
of the leading methods for the basis pursuit problem.

2 
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.

3 
Video stabilization of atmospheric turbulence distortion
Volume 7, Number 3, Pages: 839  861, 2013
Yifei Lou,
Sung Ha Kang,
Stefano Soatto
and Andrea L. Bertozzi
Abstract
References
Full Text
Related Articles
We present a method to enhance the quality of a video sequence
captured through a turbulent atmospheric medium, and give an
estimate of the radiance of the distant scene, represented as a
``latent image,'' which is assumed to be static throughout the
video. Due to atmospheric turbulence, temporal averaging produces
a blurred version of the scene's radiance. We propose a method
combining Sobolev gradient and Laplacian to stabilize the video
sequence, and a latent image is further found utilizing the ``lucky
region" method. The video sequence is stabilized while keeping
sharp details, and the latent image shows more consistent straight
edges. We analyze the wellposedness for the stabilizing PDE and the
linear stability of the numerical scheme.

4 
Detecting small low emission radiating sources
Volume 7, Number 1, Pages: 47  79, 2013
Moritz Allmaras,
David Darrow,
Yulia Hristova,
Guido Kanschat
and Peter Kuchment
Abstract
References
Full Text
Related Articles
In order to prevent influx of highly enriched nuclear material
through border checkpoints, new advanced detection schemes need to be
developed. Typical issues faced in this context are sources with very
low emission against a dominating natural background radiation. Sources
are expected to be small and shielded and hence cannot be detected from
measurements of radiation levels alone.
We consider collimated and Comptontype measurements and propose a detection
method that relies on the geometric singularity of small sources to
distinguish them from the more uniform background.
The method is characterized by high sensitivity and specificity and
allows for assigning confidence probabilities of detection.
The validity of our approach can be justified using properties of
related techniques from medical imaging. Results of numerical
simulations are presented for collimated and Comptontype measurements.
The 2D case is considered in detail.

5 
The "exterior approach" to solve the inverse obstacle problem for the Stokes system
Volume 8, Number 1, Pages: 23  51, 2014
Laurent Bourgeois
and Jérémi Dardé
Abstract
References
Full Text
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We apply an ``exterior approach" based on the coupling of a method of quasireversibility and of a level set method in order to recover a fixed obstacle immersed in a Stokes flow from boundary measurements.
Concerning the method of quasireversibility, two new mixed formulations are introduced in order to solve the illposed Cauchy problems for the Stokes system by using some classical conforming finite elements. We provide some proofs for the convergence of the quasireversibility methods on the one hand and of the level set method on the other hand.
Some numerical experiments in $2D$ show the efficiency of the two mixed formulations and of the exterior approach based on one of them.

6 
A MumfordShah levelset approach for the inversion and
segmentation of SPECT/CT data
Volume 5, Number 1, Pages: 137  166, 2011
Esther Klann,
Ronny Ramlau
and Wolfgang Ring
Abstract
References
Full Text
Related Articles
This paper presents a levelset based approach for the simultaneous reconstruction and segmentation of the activity as well as the density distribution from tomography data gathered by an integrated SPECT/CT scanner.
Activity and density distributions are modeled as piecewise constant functions. The segmenting contours and the corresponding function values of both the activity and the density distribution are found as minimizers of a MumfordShah like functional over the set of admissible contours and  for fixed contours  over the spaces of piecewise constant density and activity distributions which may be discontinuous across their corresponding contours. For the latter step a Newton method is used to solve the nonlinear optimality system. Shape sensitivity calculus is used to find a descent direction for the cost functional with respect to the geometrical variables which leads to an update formula for the contours in the levelset framework. A heuristic approach for the insertion of new components for the activity as well as the density function is used. The method is tested for synthetic data with different noise levels.

7 
Adaptive meshing approach to identification of cracks with
electrical impedance tomography
Volume 8, Number 1, Pages: 127  148, 2014
Kimmo Karhunen,
Aku Seppänen
and Jari P. Kaipio
Abstract
References
Full Text
Related Articles
Electrical impedance tomography (EIT) is a noninvasive imaging
modality in which the internal conductivity distribution
is reconstructed
based on boundary voltage measurements.
In this work, we consider the
application of EIT to nondestructive testing (NDT) of materials and,
especially, crack detection.
The main goal is to estimate the location, depth
and orientation of a crack in three dimensions.
We formulate the crack detection task as a shape estimation problem for
boundaries imposed with Neumann zero boundary conditions.
We propose an adaptive meshing algorithm that iteratively
seeks the maximum a posteriori estimate for the shape of the crack.
The approach is tested both numerically and experimentally.
In all test cases, the EIT measurements
are collected using a set of electrodes attached on only
a single planar surface of the target 
this is often the only realizable configuration in NDT of
large building structures,
such as concrete walls.
The results show that with the proposed computational method,
it is possible to recover the position and size of the crack,
even in cases where the background conductivity is inhomogeneous.

8 
Bayesian inverse problems with Monte Carlo forward models
Volume 7, Number 1, Pages: 81  105, 2013
Guillaume Bal,
Ian Langmore
and Youssef Marzouk
Abstract
References
Full Text
Related Articles
The full application of Bayesian inference to inverse
problems requires exploration of a posterior distribution that typically
does not possess a standard form. In this context, Markov chain
Monte Carlo (MCMC) methods are often used. These methods require
many evaluations of a computationally intensive forward model to
produce the equivalent of one independent sample from the posterior.
We consider applications in which approximate forward models at
multiple resolution levels are available, each endowed with a
probabilistic error estimate. These situations occur, for example,
when the forward model involves Monte Carlo integration. We present a novel
MCMC method called $MC^3$ that uses lowresolution forward
models to approximate draws from a posterior distribution built with the
highresolution forward model. The acceptance ratio is
estimated with some statistical error; then a confidence interval
for the true acceptance ratio is found, and acceptance is performed
correctly with some confidence. The highresolution models are
rarely run and a significant speed up is achieved.
Our multipleresolution forward models themselves are built around a
new importance sampling scheme that allows Monte Carlo forward
models to be used efficiently in inverse problems. The method is
used to solve an inverse transport problem that finds applications
in atmospheric remote sensing. We present a pathrecycling
methodology to efficiently vary parameters in the transport
equation. The forward transport equation is solved by a Monte Carlo
method that is amenable to the use of $MC^3$ to solve the inverse
transport problem using a Bayesian formalism.

9 
Image denoising: Learning the noise model via nonsmooth PDEconstrained optimization
Volume 7, Number 4, Pages: 1183  1214, 2013
Juan Carlos De los Reyes
and CarolaBibiane Schönlieb
Abstract
References
Full Text
Related Articles
We propose a nonsmooth PDEconstrained optimization approach for the determination of the correct
noise model in total variation (TV) image denoising. An
optimization problem for the determination of the weights
corresponding to different types of noise distributions is stated and existence of an optimal solution is
proved. A tailored regularization approach for the approximation of the optimal
parameter values is proposed thereafter and its consistency
studied. Additionally, the differentiability of the solution operator
is proved and an optimality system characterizing the optimal
solutions of each regularized problem is derived. The optimal parameter values are numerically computed by using a
quasiNewton method, together with semismooth Newton type algorithms for the solution of the TVsubproblems.

10 
Augmented Lagrangian method for a mean curvature based image denoising model
Volume 7, Number 4, Pages: 1409  1432, 2013
Wei Zhu,
XueCheng Tai
and Tony Chan
Abstract
References
Full Text
Related Articles
High order derivative information has been widely used in developing variational models in image processing to accomplish more advanced tasks. However, it is a nontrivial issue to construct efficient numerical algorithms to deal with the minimization of these variational models due to the associated high order EulerLagrange equations. In this paper, we propose an efficient numerical method for a mean curvature based image denoising model using the augmented Lagrangian method. A special technique is introduced to handle the mean curvature model for the augmented Lagrangian scheme. We detail the procedures of finding the related saddlepoints of the functional. We present numerical experiments to illustrate the effectiveness and efficiency of the proposed numerical method, and show a few important features of the image denoising model such as keeping corners and image contrast. Moreover, a comparison with the gradient descent method further demonstrates the efficiency of the proposed augmented Lagrangian method.

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