11,365 research outputs found
Joint Image Reconstruction and Segmentation Using the Potts Model
We propose a new algorithmic approach to the non-smooth and non-convex Potts
problem (also called piecewise-constant Mumford-Shah problem) for inverse
imaging problems. We derive a suitable splitting into specific subproblems that
can all be solved efficiently. Our method does not require a priori knowledge
on the gray levels nor on the number of segments of the reconstruction.
Further, it avoids anisotropic artifacts such as geometric staircasing. We
demonstrate the suitability of our method for joint image reconstruction and
segmentation. We focus on Radon data, where we in particular consider limited
data situations. For instance, our method is able to recover all segments of
the Shepp-Logan phantom from angular views only. We illustrate the
practical applicability on a real PET dataset. As further applications, we
consider spherical Radon data as well as blurred data
Superiorization and Perturbation Resilience of Algorithms: A Continuously Updated Bibliography
This document presents a, (mostly) chronologically ordered, bibliography of
scientific publications on the superiorization methodology and perturbation
resilience of algorithms which is compiled and continuously updated by us at:
http://math.haifa.ac.il/yair/bib-superiorization-censor.html. Since the
beginings of this topic we try to trace the work that has been published about
it since its inception. To the best of our knowledge this bibliography
represents all available publications on this topic to date, and while the URL
is continuously updated we will revise this document and bring it up to date on
arXiv approximately once a year. Abstracts of the cited works, and some links
and downloadable files of preprints or reprints are available on the above
mentioned Internet page. If you know of a related scientific work in any form
that should be included here kindly write to me on: [email protected] with
full bibliographic details, a DOI if available, and a PDF copy of the work if
possible. The Internet page was initiated on March 7, 2015, and has been last
updated on March 12, 2020.Comment: Original report: June 13, 2015 contained 41 items. First revision:
March 9, 2017 contained 64 items. Second revision: March 8, 2018 contained 76
items. Third revision: March 11, 2019 contains 90 items. Fourth revision:
March 16, 2020 contains 112 item
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
Compressive sampling offers a new paradigm for acquiring signals that are
compressible with respect to an orthonormal basis. The major algorithmic
challenge in compressive sampling is to approximate a compressible signal from
noisy samples. This paper describes a new iterative recovery algorithm called
CoSaMP that delivers the same guarantees as the best optimization-based
approaches. Moreover, this algorithm offers rigorous bounds on computational
cost and storage. It is likely to be extremely efficient for practical problems
because it requires only matrix-vector multiplies with the sampling matrix. For
many cases of interest, the running time is just O(N*log^2(N)), where N is the
length of the signal.Comment: 30 pages. Revised. Presented at Information Theory and Applications,
31 January 2008, San Dieg
An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems
We propose a new fast algorithm for solving one of the standard approaches to
ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth)
regularizer is minimized under the constraint that the solution explains the
observations sufficiently well. Although the regularizer and constraint are
usually convex, several particular features of these problems (huge
dimensionality, non-smoothness) preclude the use of off-the-shelf optimization
tools and have stimulated a considerable amount of research. In this paper, we
propose a new efficient algorithm to handle one class of constrained problems
(often known as basis pursuit denoising) tailored to image recovery
applications. The proposed algorithm, which belongs to the family of augmented
Lagrangian methods, can be used to deal with a variety of imaging IPLIP,
including deconvolution and reconstruction from compressive observations (such
as MRI), using either total-variation or wavelet-based (or, more generally,
frame-based) regularization. The proposed algorithm is an instance of the
so-called "alternating direction method of multipliers", for which convergence
sufficient conditions are known; we show that these conditions are satisfied by
the proposed algorithm. Experiments on a set of image restoration and
reconstruction benchmark problems show that the proposed algorithm is a strong
contender for the state-of-the-art.Comment: 13 pages, 8 figure, 8 tables. Submitted to the IEEE Transactions on
Image Processin
Direct Numerical Simulation of Complex Multi-Fluid Flows Using a Combined Volume of Fluid and Immersed Boundary Method
In this paper a simulation model is presented for the Direct Numerical Simulation (DNS) of complex multi-fluid flows in which simultaneously (moving) deformable (drops or bubbles) and non-deformable (moving) elements (particles) are present, possibly with the additional presence of free surfaces. Our model combines the VOF model developed by van Sint Annaland et al. (2005) and the Immersed Boundary (IB) model developed by van der Hoef et al. (2006). The Volume of Fluid (VOF) part features i) an interface reconstruction technique based on piecewise linear interface representation ii) a three-dimensional version of the CSF model of Brackbill et al. (1992). The Immersed Boundary (IB) part incorporates both particle-fluid and particle-particle interaction via a Direct Forcing Method (DFM) and a hard sphere Discrete Particle (DP) approach. In our model a fixed (Eulerian) grid is utilized to solve the Navier-Stokes equations for the entire computational domain. The no-slip condition at the surface of the moving particles is enforced via a momentum source term which only acts in the vicinity of the particle surface. For the enforcement of the no-slip condition Lagrangian force points are used which are distributed evenly over the surface of the particle. Dissipative particle-particle and/or particle-wall collisions are accounted via a hard sphere DP approach (Hoomans et al., 1996) using a three-parameter particle-particle interaction model accounting for normal and tangential restitution and tangential friction. The capabilities of the hybrid VOF-IB model are demonstrated with a number of examples in which complex topological changes in the interface are encountered
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