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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 2016 in February, May, August and November.
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TOP 10 Most Read Articles in IPI, December 2016
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 
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.

5 
Heat source identification based on $l_1$ constrained minimization
Volume 8, Number 1, Pages: 199  221, 2014
Yingying Li,
Stanley Osher
and Richard Tsai
Abstract
References
Full Text
Related Articles
We consider the inverse problem of finding sparse initial data from the
sparsely sampled solutions of the heat equation. The initial data are assumed
to be a sum of an unknown but finite number of Dirac delta functions at unknown locations.
Pointwise values of the heat solution at only a few locations are used in an
$l_1$ constrained optimization to find the initial data. A concept of
domain of effective sensing is introduced to speed up the already fast Bregman
iterative algorithm for $l_1$ optimization. Furthermore, an algorithm which
successively adds new measurements at specially chosen locations is introduced. By
comparing the solutions of the inverse problem obtained from different number of
measurements, the algorithm decides where to add new measurements in order to
improve the reconstruction of the sparse initial data.

6 
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
Related Articles
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.

7 
Convergence rates for Kaczmarztype regularization methods
Volume 8, Number 1, Pages: 149  172, 2014
Stefan Kindermann
and Antonio Leitão
Abstract
References
Full Text
Related Articles
This article is devoted to the convergence analysis of a special family of iterative
regularization methods for solving systems of illposed operator equations in Hilbert
spaces, namely Kaczmarztype methods.
The analysis is focused on the LandweberKaczmarz (LK) explicit iteration and the
iterated TikhonovKaczmarz (iTK) implicit iteration. The corresponding symmetric
versions of these iterative methods are also investigated (sLK and siTK).
We prove convergence rates for the four methods above, extending and complementing the
convergence analysis established originally in [22,13,12,8].

8 
Imaging of unknown targets inside inhomogeneous backgrounds by means of qualitative inverse scattering
Volume 3, Number 2, Pages: 231  241, 2009
Giovanni Bozza,
Massimo Brignone,
Matteo Pastorino,
Andrea Randazzo
and Michele Piana
Abstract
Full Text
Related Articles
In this paper a new formulation of the Linear Sampling Method, called the noSampling Linear Sampling
Method, is applied to the imaging and detection of unknown scatterers located inside an inhomogeneous
background. Namely, by following a previous work by Colton and Monk, a modified farfield equation
is used, which allows one to use line current sources and nearfield measurements. The Green's function
of the inhomogeneous background is numerically computed and used as the right hand side of the modified farfield
equation. The proposed method is then applied to two different scenarios: the detection of breast tumors and
the imaging of cracks inside a dielectric slab. A numerical analysis of the method capabilities is performed when the
model parameters are not exactly known.

9 
The Moreau envelope approach for the L1/TV image denoising model
Volume 8, Number 1, Pages: 53  77, 2014
Feishe Chen,
Lixin Shen,
Yuesheng Xu
and Xueying Zeng
Abstract
References
Full Text
Related Articles
This paper presents the Moreau envelope viewpoint for the L1/TV
image denoising model. The main algorithmic difficulty for the
numerical treatment of the L1/TV model lies in the
nondifferentiability of both the fidelity and regularization terms
of the model. To overcome this difficulty, we propose five modified
L1/TV models by replacing one or two nondifferentiable
functions in the L1/TV model with their corresponding Moreau
envelopes. We prove that several existing approaches for the L1/TV
model essentially solve some of the modified models, but not the
original L1/TV model. Algorithms for the L1/TV model and its five
variants are proposed under a unified framework based on fixedpoint equations (via the
proximity operator) which characterize the solutions of the models. Depending upon whether we smooth the
regularization term or not, two different types of proximity
algorithms are presented. The convergence rates of both types of the
algorithms are improved significantly by exploring either the
strategy of the GaussSeidel iteration, or the FISTA, or both. We
compare the performance of various modified L1/TV models for the
problem of impulse noise removal, and make recommendations based on
our numerical experiments for using these models in applications.

10 
PHLST with adaptive tiling and its application to
antarctic remote sensing image approximation
Volume 8, Number 1, Pages: 321  337, 2014
Zhihua Zhang
and Naoki Saito
Abstract
References
Full Text
Related Articles
We propose an efficient nonlinear approximation scheme using the
Polyharmonic Local Sine Transform (PHLST) of Saito and Remy combined
with an algorithm to tile a given image automatically and adaptively
according to its local smoothness and singularities. To measure such
local smoothness, we introduce the socalled local Besov indices of
an image, which is based on the pointwise modulus of smoothness of
the image. Such an adaptive tiling of an image is important for
image approximation using PHLST because PHLST stores the corner and
boundary information of each tile and consequently it is wasteful to
divide a smooth region of a given image into a set of smaller tiles.
We demonstrate the superiority of the proposed algorithm using
Antarctic remote sensing images over the PHLST using the uniform
tiling. Analysis of such images including their efficient
approximation and compression has gained its importance due to the
global climate change.

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