Time-resolved characterization of a pulsed discharge in a stationary bubble

In recent years, plasma generation in water has been proposed for the application of water treatment. The process efficiency is believed to be improved by the introduction of bubbles in the plasma active region. For further optimization, the initiating and developmental mechanisms of plasma inside bubbles need to be understood to a greater extent. In order to meet this necessity, we investigated pulsed electrical discharge inside a stationary bubble in water. This paper deals with the evolution of the discharge and of the bubble shape during discharge, investigated by electrical characterization and fast imaging. Only several microseconds after the application of the voltage pulse, plasma light is observed. Different phases are observed during plasma formation. The plasma is strongest at the bubble surface, causing the surrounding water to evaporate. This leads to both the formation of propagating streamers into the water and the expansion and collapse of the bubble. These observations show that plasma inside a bubble has the strongest activity at the bubble surface, making it attractive for water treatment

SUBDIVIDE AND CONQUER RESOLUTION

This contribution will be freewheeling in the domain of signal, image and surface processing and touch briefly upon some topics that have been close to the heart of people in our research group. A lot of the research of the last 20 years in this domain that has been carried out world wide is dealing with multiresolution. Multiresolution allows to represent a function (in the broadest sense) at different levels of detail. This was not only applied in signals and images but also when solving all kinds of complex numerical problems. Since wavelets came into play in the 1980's, this idea was applied and generalized by many researchers. Therefore we use this as the central idea throughout this text. Wavelets, subdivision and hierarchical bases are the appropriate tools to obtain these multiresolution effects. We shall introduce some of the concepts in a rather informal way and show that the same concepts will work in one, two and three dimensions. The applications in the three cases are however quite different, and thus one wants to achieve very different goals when dealing with signals, images or surfaces. Because completeness in our treatment is impossible, we have chosen to describe two case studies after introducing some concepts in signal processing. These case studies are still the subject of current research. The first one attempts to solve a problem in image processing: how to approximate an edge in an image efficiently by subdivision. The method is based on normal offsets. The second case is the use of Powell-Sabin splines to give a smooth multiresolution representation of a surface. In this context we also illustrate the general method of construction of a spline wavelet basis using a lifting scheme

Stabilizing wavelet transforms for non-equispaced data smoothing

info:eu-repo/semantics/publishe

<title>Stabilized lifting steps in noise reduction for nonequispaced samples</title>

This paper discusses wavelet thresholding in smoothing from non-equispaced, noisy data in one dimension. To deal with the irregularity of the grid we use so called second generation wavelets, based on the lifting scheme. We explain that a good numerical condition is an absolute requisite for successful thresholding. If this condition is not satisfied the output signal can show an arbitrary bias. We examine the nature and origin of stability problems in second generation wavelet transforms. The investigation concentrates on lifting with interpolating prediction, but the conclusions are extendible. The stability problem is a cumulated effect of the three successive steps in a lifting scheme: split, predict and update. The paper proposes three ways to stabilize the second generation wavelet transform. The first is a change in update and reduces the influence of the previous steps. The second is a change in prediction and operates on the interval boundaries. The third is a change in splitting procedure and concentrates on the irregularity of the data points. Illustrations show that reconstruction from thresholded coefficients with this stabilized second generation wavelet transform leads to smooth and close fit

Image compression using normal mesh techniques

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Multiscale Local Polynomial Models for Estimation and Testing

We present a wavelet-like multiscale decomposition based on iterated local polynomial smoothing with scale dependent bandwidths. For reasons of continuity and smoothness, a multiscale smoothing decomposition must be slightly overcomplete, but the redundancy is less than in the nondecimated wavelet transform. Unlike decimated wavelet transforms, multiscale local polynomial decompositions remain numerically stable and the reconstructions are still smooth when the decomposition is applied to time series data on irregular time points. In image denoising, local polynomials outperform nondecimated wavelet transforms, even though the latter have a higher degree of redundancy allowing additional smoothing upon reconstruction. Another benefit from the presented scheme is its ability to construct multiscale decompositions for derivatives of functions. The transform can also be extended towards nonlinear and observation-adaptive data decompositions.SCOPUS: cp.pinfo:eu-repo/semantics/publishe