1,867 research outputs found
Extraction of coherent structures in a rotating turbulent flow experiment
The discrete wavelet packet transform (DWPT) and discrete wavelet transform
(DWT) are used to extract and study the dynamics of coherent structures in a
turbulent rotating fluid. Three-dimensional (3D) turbulence is generated by
strong pumping through tubes at the bottom of a rotating tank (48.4 cm high,
39.4 cm diameter). This flow evolves toward two-dimensional (2D) turbulence
with increasing height in the tank. Particle Image Velocimetry (PIV)
measurements on the quasi-2D flow reveal many long-lived coherent vortices with
a wide range of sizes. The vorticity fields exhibit vortex birth, merger,
scattering, and destruction. We separate the flow into a low-entropy
``coherent'' and a high-entropy ``incoherent'' component by thresholding the
coefficients of the DWPT and DWT of the vorticity fields. Similar thresholdings
using the Fourier transform and JPEG compression together with the Okubo-Weiss
criterion are also tested for comparison. We find that the DWPT and DWT yield
similar results and are much more efficient at representing the total flow than
a Fourier-based method. Only about 3% of the large-amplitude coefficients of
the DWPT and DWT are necessary to represent the coherent component and preserve
the vorticity probability density function, transport properties, and spatial
and temporal correlations. The remaining small amplitude coefficients represent
the incoherent component, which has near Gaussian vorticity PDF, contains no
coherent structures, rapidly loses correlation in time, and does not contribute
significantly to the transport properties of the flow. This suggests that one
can describe and simulate such turbulent flow using a relatively small number
of wavelet or wavelet packet modes.Comment: experimental work aprox 17 pages, 11 figures, accepted to appear in
PRE, last few figures appear at the end. clarifications, added references,
fixed typo
Deep Graph Laplacian Regularization for Robust Denoising of Real Images
Recent developments in deep learning have revolutionized the paradigm of
image restoration. However, its applications on real image denoising are still
limited, due to its sensitivity to training data and the complex nature of real
image noise. In this work, we combine the robustness merit of model-based
approaches and the learning power of data-driven approaches for real image
denoising. Specifically, by integrating graph Laplacian regularization as a
trainable module into a deep learning framework, we are less susceptible to
overfitting than pure CNN-based approaches, achieving higher robustness to
small datasets and cross-domain denoising. First, a sparse neighborhood graph
is built from the output of a convolutional neural network (CNN). Then the
image is restored by solving an unconstrained quadratic programming problem,
using a corresponding graph Laplacian regularizer as a prior term. The proposed
restoration pipeline is fully differentiable and hence can be end-to-end
trained. Experimental results demonstrate that our work is less prone to
overfitting given small training data. It is also endowed with strong
cross-domain generalization power, outperforming the state-of-the-art
approaches by a remarkable margin
On Kernel Selection of Multivariate Local Polynomial Modelling and its Application to Image Smoothing and Reconstruction
This paper studies the problem of adaptive kernel selection for multivariate local polynomial regression (LPR) and its application to smoothing and reconstruction of noisy images. In multivariate LPR, the multidimensional signals are modeled locally by a polynomial using least-squares (LS) criterion with a kernel controlled by a certain bandwidth matrix. Based on the traditional intersection confidence intervals (ICI) method, a new refined ICI (RICI) adaptive scale selector for symmetric kernel is developed to achieve a better bias-variance tradeoff. The method is further extended to steering kernel with local orientation to adapt better to local characteristics of multidimensional signals. The resulting multivariate LPR method called the steering-kernel-based LPR with refined ICI method (SK-LPR-RICI) is applied to the smoothing and reconstruction problems in noisy images. Simulation results show that the proposed SK-LPR-RICI method has a better PSNR and visual performance than conventional LPR-based methods in image processing. © 2010 The Author(s).published_or_final_versio
A wavelet add-on code for new-generation N-body simulations and data de-noising (JOFILUREN)
Wavelets are a new and powerful mathematical tool, whose most celebrated
applications are data compression and de-noising. In Paper I (Romeo, Horellou &
Bergh 2003, astro-ph/0302343), we have shown that wavelets can be used for
removing noise efficiently from cosmological, galaxy and plasma N-body
simulations. The expected two-orders-of-magnitude higher performance means, in
terms of the well-known Moore's law, an advance of more than one decade in the
future. In this paper, we describe a wavelet add-on code designed for such an
application. Our code can be included in common grid-based N-body codes, is
written in Fortran, is portable and available on request from the first author.
The code can also be applied for removing noise from standard data, such as
signals and images.Comment: Mon. Not. R. Astron. Soc., in press. The interested reader is
strongly recommended to ignore the low-resolution Figs 10 and 11, and to
download the full-resolution paper (800 kb) from
http://www.oso.chalmers.se/~romeo/Paper_VII.ps.g
De-noising by thresholding operator adapted wavelets
Donoho and Johnstone proposed a method from reconstructing an unknown smooth
function from noisy data by translating the empirical wavelet
coefficients of towards zero. We consider the situation where the
prior information on the unknown function may not be the regularity of
but that of \L u where \L is a linear operator (such as a PDE or a graph
Laplacian). We show that the approximation of obtained by thresholding the
gamblet (operator adapted wavelet) coefficients of is near minimax
optimal (up to a multiplicative constant), and with high probability, its
energy norm (defined by the operator) is bounded by that of up to a
constant depending on the amplitude of the noise. Since gamblets can be
computed in complexity and are
localized both in space and eigenspace, the proposed method is of near-linear
complexity and generalizable to non-homogeneous noise
A Second Order TV-type Approach for Inpainting and Denoising Higher Dimensional Combined Cyclic and Vector Space Data
In this paper we consider denoising and inpainting problems for higher
dimensional combined cyclic and linear space valued data. These kind of data
appear when dealing with nonlinear color spaces such as HSV, and they can be
obtained by changing the space domain of, e.g., an optical flow field to polar
coordinates. For such nonlinear data spaces, we develop algorithms for the
solution of the corresponding second order total variation (TV) type problems
for denoising, inpainting as well as the combination of both. We provide a
convergence analysis and we apply the algorithms to concrete problems.Comment: revised submitted versio
- …