Tomographic reconstruction of tokamak plasma light emission from single image using wavelet-vaguelette decomposition

Abstract

Images acquired by cameras installed in tokamaks are difficult to interpret because the three-dimensional structure of the plasma is flattened in a non-trivial way. Nevertheless, taking advantage of the slow variation of the fluctuations along magnetic field lines, the optical transformation may be approximated by a generalized Abel transform, for which we propose an inversion technique based on the wavelet-vaguelette decomposition. After validation of the new method using an academic test case and numerical data obtained with the Tokam 2D code, we present an application to an experimental movie obtained in the tokamak Tore Supra. A comparison with a classical regularization technique for ill-posed inverse problems, the singular value decomposition, allows us to assess the efficiency. The superiority of the wavelet-vaguelette technique is reflected in preserving local features, such as blobs and fronts, in the denoised emissivity map.

Wavelet transforms and their applications to MHD and plasma turbulence: a review

“…Taking advantage of the slow variation of the fluctuations along magnetic field lines in tokamaks, this inverse problem can be modelled by a helical Abel transform, which is a Volterra integral operator of the first kind. In [33] we proposed a tomographic inversion technique, based on a wavelet-vaguelette decomposition and coupled with wavelet denoising to extract coherent structures, that allows to detect individual blobs on the projected movie and to analyse their behaviour. The wavelet-vaguelette decomposition (WVD) was introduced by Tchamitchian [43] and used by Donoho [12] to solve inverse problems in the presence of localized structures.…”

“…Right: denoised frame obtained by applying the operator K to the reconstructed emissivity map. From [33].…”

“…The technicalities of WVD are described in detail in Nguyen van yen et al. (2012), in the following we explain only the principle. The helical Abel transform related the plasma light emissivity (a scalar-valued field) to the integral of the volume emissivity received by the camera , where is a compact continuous operator.…”

“…( c ) Noisy image obtained by adding Gaussian white noise with variance 0.5 (from Nguyen van yen et al. 2012). …”

Wavelet methods for studying the onset of strong plasma turbulence

“…Wavelet-based density estimation techniques have also been used to improve particle-in-cell numerical schemes [11], and a particle-in-wavelet scheme was developed for solving the Vlasov-Poisson equations directly in wavelet space [12]. Wavelet de-noising has been applied for tomographic reconstruction of tokamak plasma light emission in [13]. Coherent Vorticity and Current sheet Simulation (CVCS), which applies wavelet filtering to the resistive non-ideal MHD equations, was proposed as a new model for turbulent MHD flows.…”