12,358 research outputs found
A Bayesian fusion model for space-time reconstruction of finely resolved velocities in turbulent flows from low resolution measurements
The study of turbulent flows calls for measurements with high resolution both
in space and in time. We propose a new approach to reconstruct
High-Temporal-High-Spatial resolution velocity fields by combining two sources
of information that are well-resolved either in space or in time, the
Low-Temporal-High-Spatial (LTHS) and the High-Temporal-Low-Spatial (HTLS)
resolution measurements. In the framework of co-conception between sensing and
data post-processing, this work extensively investigates a Bayesian
reconstruction approach using a simulated database. A Bayesian fusion model is
developed to solve the inverse problem of data reconstruction. The model uses a
Maximum A Posteriori estimate, which yields the most probable field knowing the
measurements. The DNS of a wall-bounded turbulent flow at moderate Reynolds
number is used to validate and assess the performances of the present approach.
Low resolution measurements are subsampled in time and space from the fully
resolved data. Reconstructed velocities are compared to the reference DNS to
estimate the reconstruction errors. The model is compared to other conventional
methods such as Linear Stochastic Estimation and cubic spline interpolation.
Results show the superior accuracy of the proposed method in all
configurations. Further investigations of model performances on various range
of scales demonstrate its robustness. Numerical experiments also permit to
estimate the expected maximum information level corresponding to limitations of
experimental instruments.Comment: 15 pages, 6 figure
Frequency Analysis of Gradient Estimators in Volume Rendering
Gradient information is used in volume rendering to classify and color samples along a ray. In this paper, we present an analysis of the theoretically ideal gradient estimator and compare it to some commonly used gradient estimators. A new method is presented to calculate the gradient at arbitrary sample positions, using the derivative of the interpolation filter as the basis for the new gradient filter. As an example, we will discuss the use of the derivative of the cubic spline. Comparisons with several other methods are demonstrated. Computational efficiency can be realized since parts of the interpolation computation can be leveraged in the gradient estimatio
Optimising Spatial and Tonal Data for PDE-based Inpainting
Some recent methods for lossy signal and image compression store only a few
selected pixels and fill in the missing structures by inpainting with a partial
differential equation (PDE). Suitable operators include the Laplacian, the
biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The
quality of such approaches depends substantially on the selection of the data
that is kept. Optimising this data in the domain and codomain gives rise to
challenging mathematical problems that shall be addressed in our work.
In the 1D case, we prove results that provide insights into the difficulty of
this problem, and we give evidence that a splitting into spatial and tonal
(i.e. function value) optimisation does hardly deteriorate the results. In the
2D setting, we present generic algorithms that achieve a high reconstruction
quality even if the specified data is very sparse. To optimise the spatial
data, we use a probabilistic sparsification, followed by a nonlocal pixel
exchange that avoids getting trapped in bad local optima. After this spatial
optimisation we perform a tonal optimisation that modifies the function values
in order to reduce the global reconstruction error. For homogeneous diffusion
inpainting, this comes down to a least squares problem for which we prove that
it has a unique solution. We demonstrate that it can be found efficiently with
a gradient descent approach that is accelerated with fast explicit diffusion
(FED) cycles. Our framework allows to specify the desired density of the
inpainting mask a priori. Moreover, is more generic than other data
optimisation approaches for the sparse inpainting problem, since it can also be
extended to nonlinear inpainting operators such as EED. This is exploited to
achieve reconstructions with state-of-the-art quality.
We also give an extensive literature survey on PDE-based image compression
methods
Single Frame Image super Resolution using Learned Directionlets
In this paper, a new directionally adaptive, learning based, single image
super resolution method using multiple direction wavelet transform, called
Directionlets is presented. This method uses directionlets to effectively
capture directional features and to extract edge information along different
directions of a set of available high resolution images .This information is
used as the training set for super resolving a low resolution input image and
the Directionlet coefficients at finer scales of its high-resolution image are
learned locally from this training set and the inverse Directionlet transform
recovers the super-resolved high resolution image. The simulation results
showed that the proposed approach outperforms standard interpolation techniques
like Cubic spline interpolation as well as standard Wavelet-based learning,
both visually and in terms of the mean squared error (mse) values. This method
gives good result with aliased images also.Comment: 14 pages,6 figure
Super-resolution of 3D Magnetic Resonance Images by Random Shifting and Convolutional Neural Networks
Enhancing resolution is a permanent goal in magnetic resonance (MR) imaging, in order to keep improving diagnostic capability and registration methods. Super-resolution (SR) techniques are applied at the postprocessing stage, and their use and development have progressively increased during the last years. In particular, example-based methods have been mostly proposed in recent state-of-the-art works. In this paper, a combination of a deep-learning SR system and a random shifting technique to improve the quality of MR images is proposed, implemented and tested. The model was compared to four competitors: cubic spline interpolation, non-local means upsampling, low-rank total variation and a three-dimensional convolutional neural network trained with patches of HR brain images (SRCNN3D). The newly proposed method showed better results in Peak Signal-to-Noise Ratio, Structural Similarity index, and Bhattacharyya coefficient. Computation times were at the
same level as those of these up-to-date methods. When applied to downsampled MR structural T1 images, the new method also yielded better qualitative results, both in the restored images and in the images of residuals.Universidad de MĂĄlaga. Campus de Excelencia Internacional AndalucĂa Tech
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