584 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
Multigrid Backprojection Super-Resolution and Deep Filter Visualization
We introduce a novel deep-learning architecture for image upscaling by large
factors (e.g. 4x, 8x) based on examples of pristine high-resolution images. Our
target is to reconstruct high-resolution images from their downscale versions.
The proposed system performs a multi-level progressive upscaling, starting from
small factors (2x) and updating for higher factors (4x and 8x). The system is
recursive as it repeats the same procedure at each level. It is also residual
since we use the network to update the outputs of a classic upscaler. The
network residuals are improved by Iterative Back-Projections (IBP) computed in
the features of a convolutional network. To work in multiple levels we extend
the standard back-projection algorithm using a recursion analogous to
Multi-Grid algorithms commonly used as solvers of large systems of linear
equations. We finally show how the network can be interpreted as a standard
upsampling-and-filter upscaler with a space-variant filter that adapts to the
geometry. This approach allows us to visualize how the network learns to
upscale. Finally, our system reaches state of the art quality for models with
relatively few number of parameters.Comment: Spotlight paper in the Thirty-Third AAAI Conference on Artificial
Intelligence (AAAI-19
A novel variational model for image registration using Gaussian curvature
Image registration is one important task in many image processing
applications. It aims to align two or more images so that useful information
can be extracted through comparison, combination or superposition. This is
achieved by constructing an optimal trans- formation which ensures that the
template image becomes similar to a given reference image. Although many models
exist, designing a model capable of modelling large and smooth deformation
field continues to pose a challenge. This paper proposes a novel variational
model for image registration using the Gaussian curvature as a regulariser. The
model is motivated by the surface restoration work in geometric processing
[Elsey and Esedoglu, Multiscale Model. Simul., (2009), pp. 1549-1573]. An
effective numerical solver is provided for the model using an augmented
Lagrangian method. Numerical experiments can show that the new model
outperforms three competing models based on, respectively, a linear curvature
[Fischer and Modersitzki, J. Math. Imaging Vis., (2003), pp. 81- 85], the mean
curvature [Chumchob, Chen and Brito, Multiscale Model. Simul., (2011), pp.
89-128] and the diffeomorphic demon model [Vercauteren at al., NeuroImage,
(2009), pp. 61-72] in terms of robustness and accuracy.Comment: 23 pages, 5 figures. Key words: Image registration, Non-parametric
image registration, Regularisation, Gaussian curvature, surface mappin
Enhancing Compressed Sensing 4D Photoacoustic Tomography by Simultaneous Motion Estimation
A crucial limitation of current high-resolution 3D photoacoustic tomography
(PAT) devices that employ sequential scanning is their long acquisition time.
In previous work, we demonstrated how to use compressed sensing techniques to
improve upon this: images with good spatial resolution and contrast can be
obtained from suitably sub-sampled PAT data acquired by novel acoustic scanning
systems if sparsity-constrained image reconstruction techniques such as total
variation regularization are used. Now, we show how a further increase of image
quality can be achieved for imaging dynamic processes in living tissue (4D
PAT). The key idea is to exploit the additional temporal redundancy of the data
by coupling the previously used spatial image reconstruction models with
sparsity-constrained motion estimation models. While simulated data from a
two-dimensional numerical phantom will be used to illustrate the main
properties of this recently developed
joint-image-reconstruction-and-motion-estimation framework, measured data from
a dynamic experimental phantom will also be used to demonstrate their potential
for challenging, large-scale, real-world, three-dimensional scenarios. The
latter only becomes feasible if a carefully designed combination of tailored
optimization schemes is employed, which we describe and examine in more detail
Colour image segmentation by the vector-valued Allen-Cahn phase-field model: a multigrid solution
We propose a new method for the numerical solution of a PDE-driven model for
colour image segmentation and give numerical examples of the results. The
method combines the vector-valued Allen-Cahn phase field equation with initial
data fitting terms. This method is known to be closely related to the
Mumford-Shah problem and the level set segmentation by Chan and Vese. Our
numerical solution is performed using a multigrid splitting of a finite element
space, thereby producing an efficient and robust method for the segmentation of
large images.Comment: 17 pages, 9 figure
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