1,240 research outputs found
A variational algorithm for the detection of line segments
In this paper we propose an algorithm for the detection of edges in images
that is based on topological asymptotic analysis. Motivated from the
Mumford--Shah functional, we consider a variational functional that penalizes
oscillations outside some approximate edge set, which we represent as the union
of a finite number of thin strips, the width of which is an order of magnitude
smaller than their length. In order to find a near optimal placement of these
strips, we compute an asymptotic expansion of the functional with respect to
the strip size. This expansion is then employed for defining a (topological)
gradient descent like minimization method. As opposed to a recently proposed
method by some of the authors, which uses coverings with balls, the usage of
strips includes some directional information into the method, which can be used
for obtaining finer edges and can also result in a reduction of computation
times
A Reconstruction Algorithm for Photoacoustic Imaging based on the Nonuniform FFT
Fourier reconstruction algorithms significantly outperform conventional
back-projection algorithms in terms of computation time. In photoacoustic
imaging, these methods require interpolation in the Fourier space domain, which
creates artifacts in reconstructed images. We propose a novel reconstruction
algorithm that applies the one-dimensional nonuniform fast Fourier transform to
photoacoustic imaging. It is shown theoretically and numerically that our
algorithm avoids artifacts while preserving the computational effectiveness of
Fourier reconstruction.Comment: 22 pages, 8 figure
Local Analysis of Inverse Problems: H\"{o}lder Stability and Iterative Reconstruction
We consider a class of inverse problems defined by a nonlinear map from
parameter or model functions to the data. We assume that solutions exist. The
space of model functions is a Banach space which is smooth and uniformly
convex; however, the data space can be an arbitrary Banach space. We study
sequences of parameter functions generated by a nonlinear Landweber iteration
and conditions under which these strongly converge, locally, to the solutions
within an appropriate distance. We express the conditions for convergence in
terms of H\"{o}lder stability of the inverse maps, which ties naturally to the
analysis of inverse problems
Nonparametric instrumental regression with non-convex constraints
This paper considers the nonparametric regression model with an additive
error that is dependent on the explanatory variables. As is common in empirical
studies in epidemiology and economics, it also supposes that valid instrumental
variables are observed. A classical example in microeconomics considers the
consumer demand function as a function of the price of goods and the income,
both variables often considered as endogenous. In this framework, the economic
theory also imposes shape restrictions on the demand function, like
integrability conditions. Motivated by this illustration in microeconomics, we
study an estimator of a nonparametric constrained regression function using
instrumental variables by means of Tikhonov regularization. We derive rates of
convergence for the regularized model both in a deterministic and stochastic
setting under the assumption that the true regression function satisfies a
projected source condition including, because of the non-convexity of the
imposed constraints, an additional smallness condition
Controlling Complex Langevin simulations of lattice models by boundary term analysis
One reason for the well known fact that the Complex Langevin (CL) method
sometimes fails to converge or converges to the wrong limit has been identified
long ago: it is insufficient decay of the probability density either near
infinity or near poles of the drift, leading to boundary terms that spoil the
formal argument for correctness. To gain a deeper understanding of this
phenomenon, in a previous paper we have studied the emergence of such boundary
terms thoroughly in a simple model, where analytic results can be compared with
numerics. Here we continue this type of analysis for more physically
interesting models, focusing on the boundaries at infinity. We start with
abelian and non-abelian one-plaquette models, then we proceed to a Polyakov
chain model and finally to high density QCD (HDQCD) and the 3D XY model. We
show that the direct estimation of the systematic error of the CL method using
boundary terms is in principle possible.Comment: 17 pages, 11 figure
Automatic detection of arcs and arclets formed by gravitational lensing
We present an algorithm developed particularly to detect gravitationally
lensed arcs in clusters of galaxies. This algorithm is suited for automated
surveys as well as individual arc detections. New methods are used for image
smoothing and source detection. The smoothing is performed by so-called
anisotropic diffusion, which maintains the shape of the arcs and does not
disperse them. The algorithm is much more efficient in detecting arcs than
other source finding algorithms and the detection by eye.Comment: A&A in press, 12 pages, 16 figure
Fast parallel algorithms for a broad class of nonlinear variational diffusion approaches
Variational segmentation and nonlinear diffusion approaches have been very active research areas in the fields of image processing and computer vision during the last years. In the present paper, we review recent advances in the development of efficient numerical algorithms for these approaches. The performance of parallel implement at ions of these algorithms on general-purpose hardware is assessed. A mathematically clear connection between variational models and nonlinear diffusion filters is presented that allows to interpret one approach as an approximation of the other, and vice versa. Numerical results confirm that, depending on the parametrization, this approximation can be made quite accurate. Our results provide a perspective for uniform implement at ions of both nonlinear variational models and diffusion filters on parallel architectures
A Dynamic Programming Solution to Bounded Dejittering Problems
We propose a dynamic programming solution to image dejittering problems with
bounded displacements and obtain efficient algorithms for the removal of line
jitter, line pixel jitter, and pixel jitter.Comment: The final publication is available at link.springer.co
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