368 research outputs found
Implementation of an Optimal First-Order Method for Strongly Convex Total Variation Regularization
We present a practical implementation of an optimal first-order method, due
to Nesterov, for large-scale total variation regularization in tomographic
reconstruction, image deblurring, etc. The algorithm applies to -strongly
convex objective functions with -Lipschitz continuous gradient. In the
framework of Nesterov both and are assumed known -- an assumption
that is seldom satisfied in practice. We propose to incorporate mechanisms to
estimate locally sufficient and during the iterations. The mechanisms
also allow for the application to non-strongly convex functions. We discuss the
iteration complexity of several first-order methods, including the proposed
algorithm, and we use a 3D tomography problem to compare the performance of
these methods. The results show that for ill-conditioned problems solved to
high accuracy, the proposed method significantly outperforms state-of-the-art
first-order methods, as also suggested by theoretical results.Comment: 23 pages, 4 figure
Combining Contrast Invariant L1 Data Fidelities with Nonlinear Spectral Image Decomposition
This paper focuses on multi-scale approaches for variational methods and
corresponding gradient flows. Recently, for convex regularization functionals
such as total variation, new theory and algorithms for nonlinear eigenvalue
problems via nonlinear spectral decompositions have been developed. Those
methods open new directions for advanced image filtering. However, for an
effective use in image segmentation and shape decomposition, a clear
interpretation of the spectral response regarding size and intensity scales is
needed but lacking in current approaches. In this context, data
fidelities are particularly helpful due to their interesting multi-scale
properties such as contrast invariance. Hence, the novelty of this work is the
combination of -based multi-scale methods with nonlinear spectral
decompositions. We compare with scale-space methods in view of
spectral image representation and decomposition. We show that the contrast
invariant multi-scale behavior of promotes sparsity in the spectral
response providing more informative decompositions. We provide a numerical
method and analyze synthetic and biomedical images at which decomposition leads
to improved segmentation.Comment: 13 pages, 7 figures, conference SSVM 201
Iterative algorithms for total variation-like reconstructions in seismic tomography
A qualitative comparison of total variation like penalties (total variation,
Huber variant of total variation, total generalized variation, ...) is made in
the context of global seismic tomography. Both penalized and constrained
formulations of seismic recovery problems are treated. A number of simple
iterative recovery algorithms applicable to these problems are described. The
convergence speed of these algorithms is compared numerically in this setting.
For the constrained formulation a new algorithm is proposed and its convergence
is proven.Comment: 28 pages, 8 figures. Corrected sign errors in formula (25
Total Directional Variation for Video Denoising
In this paper, we propose a variational approach for video denoising, based
on a total directional variation (TDV) regulariser proposed in Parisotto et al.
(2018), for image denoising and interpolation. In the TDV regulariser, the
underlying image structure is encoded by means of weighted derivatives so as to
enhance the anisotropic structures in images, e.g. stripes or curves with a
dominant local directionality. For the extension of TDV to video denoising, the
space-time structure is captured by the volumetric structure tensor guiding the
smoothing process. We discuss this and present our whole video denoising
work-flow. Our numerical results are compared with some state-of-the-art video
denoising methods.SP acknowledges UK EPSRC grant EP/L016516/1 for the CCA DTC. CBS acknowledges support from Leverhulme Trust project on Breaking the non-convexity barrier, EPSRC grant Nr. EP/M00483X/1, the EPSRC Centre
EP/N014588/1, the RISE projects CHiPS and NoMADS, the CCIMI and the Alan Turing Institute
Integrated modeling and validation for phase change with natural convection
Water-ice systems undergoing melting develop complex spatio-temporal
interface dynamics and a non-trivial temperature field. In this contribution,
we present computational aspects of a recently conducted validation study that
aims at investigating the role of natural convection for cryo-interface
dynamics of water-ice. We will present a fixed grid model known as the enthalpy
porosity method. It is based on introducing a phase field and employs mixture
theory. The resulting PDEs are solved using a finite volume discretization. The
second part is devoted to experiments that have been conducted for model
validation. The evolving water-ice interface is tracked based on optical images
that shows both the water and the ice phase. To segment the phases, we use a
binary Mumford Shah method, which yields a piece-wise constant approximation of
the imaging data. Its jump set is the reconstruction of the measured phase
interface. Our combined simulation and segmentation effort finally enables us
to compare the modeled and measured phase interfaces continuously. We conclude
with a discussion of our findings
Solving Uncalibrated Photometric Stereo using Total Variation
International audienceEstimating the shape and appearance of an object, given one or several images, is still an open and challenging research problem called 3D-reconstruction. Among the different techniques available, photometric stereo (PS) produces highly accurate results when the lighting conditions have been identified. When these conditions are unknown, the problem becomes the so-called uncalibrated PS problem, which is ill-posed. In this paper, we will show how total variation can be used to reduce the ambiguities of uncalibrated PS, and we will study two methods for estimating the parameters of the generalized bas-relief ambiguity. These methods will be evaluated through the 3D-reconstruction of real-world objects
A combined first and second order variational approach for image reconstruction
In this paper we study a variational problem in the space of functions of
bounded Hessian. Our model constitutes a straightforward higher-order extension
of the well known ROF functional (total variation minimisation) to which we add
a non-smooth second order regulariser. It combines convex functions of the
total variation and the total variation of the first derivatives. In what
follows, we prove existence and uniqueness of minimisers of the combined model
and present the numerical solution of the corresponding discretised problem by
employing the split Bregman method. The paper is furnished with applications of
our model to image denoising, deblurring as well as image inpainting. The
obtained numerical results are compared with results obtained from total
generalised variation (TGV), infimal convolution and Euler's elastica, three
other state of the art higher-order models. The numerical discussion confirms
that the proposed higher-order model competes with models of its kind in
avoiding the creation of undesirable artifacts and blocky-like structures in
the reconstructed images -- a known disadvantage of the ROF model -- while
being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure
ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation
PIEMAP: Personalized Inverse Eikonal Model from cardiac Electro-Anatomical Maps
Electroanatomical mapping, a keystone diagnostic tool in cardiac
electrophysiology studies, can provide high-density maps of the local electric
properties of the tissue. It is therefore tempting to use such data to better
individualize current patient-specific models of the heart through a data
assimilation procedure and to extract potentially insightful information such
as conduction properties. Parameter identification for state-of-the-art cardiac
models is however a challenging task. In this work, we introduce a novel
inverse problem for inferring the anisotropic structure of the conductivity
tensor, that is fiber orientation and conduction velocity along and across
fibers, of an eikonal model for cardiac activation. The proposed method, named
PIEMAP, performed robustly with synthetic data and showed promising results
with clinical data. These results suggest that PIEMAP could be a useful
supplement in future clinical workflows of personalized therapies.Comment: 12 pages, 4 figures, 1 tabl
Existence of global strong solutions to a beam-fluid interaction system
We study an unsteady non linear fluid-structure interaction problem which is
a simplified model to describe blood flow through viscoleastic arteries. We
consider a Newtonian incompressible two-dimensional flow described by the
Navier-Stokes equations set in an unknown domain depending on the displacement
of a structure, which itself satisfies a linear viscoelastic beam equation. The
fluid and the structure are fully coupled via interface conditions prescribing
the continuity of the velocities at the fluid-structure interface and the
action-reaction principle. We prove that strong solutions to this problem are
global-in-time. We obtain in particular that contact between the viscoleastic
wall and the bottom of the fluid cavity does not occur in finite time. To our
knowledge, this is the first occurrence of a no-contact result, but also of
existence of strong solutions globally in time, in the frame of interactions
between a viscous fluid and a deformable structure
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