1,314 research outputs found
Adaptive Hierarchical Data Aggregation using Compressive Sensing (A-HDACS) for Non-smooth Data Field
Compressive Sensing (CS) has been applied successfully in a wide variety of
applications in recent years, including photography, shortwave infrared
cameras, optical system research, facial recognition, MRI, etc. In wireless
sensor networks (WSNs), significant research work has been pursued to
investigate the use of CS to reduce the amount of data communicated,
particularly in data aggregation applications and thereby improving energy
efficiency. However, most of the previous work in WSN has used CS under the
assumption that data field is smooth with negligible white Gaussian noise. In
these schemes signal sparsity is estimated globally based on the entire data
field, which is then used to determine the CS parameters. In more realistic
scenarios, where data field may have regional fluctuations or it is piecewise
smooth, existing CS based data aggregation schemes yield poor compression
efficiency. In order to take full advantage of CS in WSNs, we propose an
Adaptive Hierarchical Data Aggregation using Compressive Sensing (A-HDACS)
scheme. The proposed schemes dynamically chooses sparsity values based on
signal variations in local regions. We prove that A-HDACS enables more sensor
nodes to employ CS compared to the schemes that do not adapt to the changing
field. The simulation results also demonstrate the improvement in energy
efficiency as well as accurate signal recovery
Bilateral filter in image processing
The bilateral filter is a nonlinear filter that does spatial averaging without smoothing edges. It has shown to be an effective image denoising technique. It also can be applied to the blocking artifacts reduction. An important issue with the application of the bilateral filter is the selection of the filter parameters, which affect the results significantly. Another research interest of bilateral filter is acceleration of the computation speed. There are three main contributions of this thesis. The first contribution is an empirical study of the optimal bilateral filter parameter selection in image denoising. I propose an extension of the bilateral filter: multi resolution bilateral filter, where bilateral filtering is applied to the low-frequency sub-bands of a signal decomposed using a wavelet filter bank. The multi resolution bilateral filter is combined with wavelet thresholding to form a new image denoising framework, which turns out to be very effective in eliminating noise in real noisy images. The second contribution is that I present a spatially adaptive method to reduce compression artifacts. To avoid over-smoothing texture regions and to effectively eliminate blocking and ringing artifacts, in this paper, texture regions and block boundary discontinuities are first detected; these are then used to control/adapt the spatial and intensity parameters of the bilateral filter. The test results prove that the adaptive method can improve the quality of restored images significantly better than the standard bilateral filter. The third contribution is the improvement of the fast bilateral filter, in which I use a combination of multi windows to approximate the Gaussian filter more precisely
A Deep Fourier Residual Method for solving PDEs using Neural Networks
When using Neural Networks as trial functions to numerically solve PDEs, a key choice to be
made is the loss function to be minimised, which should ideally correspond to a norm of the error.
In multiple problems, this error norm coincides with–or is equivalent to–the H−1
-norm of the
residual; however, it is often difficult to accurately compute it. This work assumes rectangular
domains and proposes the use of a Discrete Sine/Cosine Transform to accurately and efficiently
compute the H−1 norm. The resulting Deep Fourier-based Residual (DFR) method efficiently
and accurately approximate solutions to PDEs. This is particularly useful when solutions lack
H2
regularity and methods involving strong formulations of the PDE fail. We observe that the
H1
-error is highly correlated with the discretised loss during training, which permits accurate
error estimation via the loss
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