1,018 research outputs found
A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution
To overcome the weakness of a total variation based model for image
restoration, various high order (typically second order) regularization models
have been proposed and studied recently. In this paper we analyze and test a
fractional-order derivative based total -order variation model, which
can outperform the currently popular high order regularization models. There
exist several previous works using total -order variations for image
restoration; however first no analysis is done yet and second all tested
formulations, differing from each other, utilize the zero Dirichlet boundary
conditions which are not realistic (while non-zero boundary conditions violate
definitions of fractional-order derivatives). This paper first reviews some
results of fractional-order derivatives and then analyzes the theoretical
properties of the proposed total -order variational model rigorously.
It then develops four algorithms for solving the variational problem, one based
on the variational Split-Bregman idea and three based on direct solution of the
discretise-optimization problem. Numerical experiments show that, in terms of
restoration quality and solution efficiency, the proposed model can produce
highly competitive results, for smooth images, to two established high order
models: the mean curvature and the total generalized variation.Comment: 26 page
Variational image registration by a total fractional-order variation model
In this paper, a new framework of nonlocal deformation in non-rigid image registration is presented. It is well known that many non-rigid image registration techniques may lead to unsteady deformation (e.g. not one to one) if the dissimilarity between the reference and template images is too large. We present a novel variational framework of the total fractional-order variation to derive the underlying fractional Euler-Lagrange equations and a numerical implementation combining the semi-implicit update and conjugate gradients (CG) solution to solve the nonlinear systems. Numerical experiments show that the new registration not only produces accurate and smooth solutions but also allows for a large rigid alignment, the evaluations of the new model demonstrate substantial improvements in accuracy and robustness over the conventional image registration approaches
A Multi-Grid Iterative Method for Photoacoustic Tomography
Inspired by the recent advances on minimizing nonsmooth or bound-constrained
convex functions on models using varying degrees of fidelity, we propose a line
search multigrid (MG) method for full-wave iterative image reconstruction in
photoacoustic tomography (PAT) in heterogeneous media. To compute the search
direction at each iteration, we decide between the gradient at the target
level, or alternatively an approximate error correction at a coarser level,
relying on some predefined criteria. To incorporate absorption and dispersion,
we derive the analytical adjoint directly from the first-order acoustic wave
system. The effectiveness of the proposed method is tested on a total-variation
penalized Iterative Shrinkage Thresholding algorithm (ISTA) and its accelerated
variant (FISTA), which have been used in many studies of image reconstruction
in PAT. The results show the great potential of the proposed method in
improving speed of iterative image reconstruction
Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications
We propose a new variational model in weighted Sobolev spaces with
non-standard weights and applications to image processing. We show that these
weights are, in general, not of Muckenhoupt type and therefore the classical
analysis tools may not apply. For special cases of the weights, the resulting
variational problem is known to be equivalent to the fractional Poisson
problem. The trace space for the weighted Sobolev space is identified to be
embedded in a weighted space. We propose a finite element scheme to solve
the Euler-Lagrange equations, and for the image denoising application we
propose an algorithm to identify the unknown weights. The approach is
illustrated on several test problems and it yields better results when compared
to the existing total variation techniques
Fractional-order diffusion for image reconstruction
International audienceIn this paper, a general framework based on fractional-order partial differential equations allows to solve image reconstruction problems. The algorithm presented in this work combines two previous notions: a fractional derivative implementation by Discrete Fourier Transform and the edge detection by topological gradient. The purpose of the paper is to extend some existing results in image denoising problem with fractional-order diffusion equations and presents new results in image inpainting. The results emphasize the importance of particular fractional-orders
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
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