In the last four years, a few research groups worked on the feasibility of compressive sampling (CS) in ultrasound medical imaging and several attempts of applying the CS theory may be found in the recent literature. In particular, it was shown that using iota<sub>p</sub>-norm minimization with p different from 1 provides interesting RF signal reconstruction results. In this paper, we propose to further improve this technique by processing the reconstruction in the Fourier domain. In addition, alpha -stable distributions are used to model the Fourier transforms of the RF lines. The parameter p used in the optimization process is related to the parameter alpha obtained by modelling the data (in the Fourier domain) as an alpha -stable distribution. The results obtained on experimental US images show significant reconstruction improvement compared to the previously published approach where the reconstruction was performed in the spatial domain.
We analyze, using the fluorescence spectroscopy of Eu<sup>3+</sup>, two partially disordered crystals from the langasite family:
langasite and langatate. There are two main differences between these crystals: (a) the randomly occupied positions (Ga<sup>3+</sup>
- Si<sup>4+</sup> in tetrahedral positions for langasite and Ga<sup> 3+</sup> - Ta <sup>5+</sup> in octahedral positions for langatate) and (b) the charge
difference between the ions in these positions (1e for langasite and 2e for langatate). For LGS:Eu, the presence of multiple
fluorescent centers could not be evidenced, while for LGT:Eu the splitting of the fluorescence lines clearly indicates the
presence of multiple fluorescent centers.
We describe new wavelet-based techniques for removing noise from digital images. In the proposed approaches, the subband decompositions of images are modelled using alpha-stable prior models, which have been shown to be flexible enough in order to capture the heavy-tailed nature of wavelet coefficients. For improved denoising performance interscale dependencies of coefficients should also be taken into account and we achieve this by employing bivariate stable distributions. We restrict our study to the particular cases of the isotropic stable and the sub-Gaussian distributions. Using Bayesian estimation principles, we design both the bivariate minimum absolute error (MAE) and the bivariate maximum a posteriori (MAP) processors based on alpha-stable signal statistics. We also discuss methods of estimating stable distributions parameters from noisy observations. In implementing our algorithms, we make use of the dual-tree complex wavelet transform, which features near shift-invariance and improved directional selectivity compared to the standard wavelet transform. We test our algorithms in comparison with several recently published methods and show that our proposed techniques are competitive with the best wavelet-based denoising systems.