Numerical simulation of knotted solutions for Maxwell equations.

In this work, we use the finite differences in time domain (FDTD) numerical method to compute and assess the validity of Hopf solutions, or hopfions, for the electromagnetic field equations. In these solutions, field lines form closed loops characterized by different knot topologies which are preserved during their time evolution. Hopfions have been studied extensively in the past from an analytical perspective but never, to the best of our knowledge, from a numerical approach. The implementation and validation of this technique eases the study of more complex cases of this phenomena; e.g., how these fields could interact with materials (e.g., anisotropic or nonlinear), their coupling with other physical systems (e.g., plasmas), and also opens the path on their artificial generation by different means (e.g., antenna arrays or lasers).

[Three-dimensional hybrid denoising algorithm in derivative domain for hyperspectral remote sensing imagery].

To tackle denosing problems in hyperspectral remote sensing imagery, a three-dimensional hybrid denoising algorithm in derivative domain was proposed. At first, hyperspectral imagery is transformed into spectral derivative domain where the subtle noise level can be elevated. And then in derivative domain, a wavelet based non-linear threshold denoising method, Bayes-Shrink algorithm, is performed in the two-dimensional spacial domain. In the spectral derivative domain, considering that the noise variance is different from band to band, the spectrum is smoothed using Savitzky-Golay filter instead of wavelet threshold denoising method. Finally, the data smoothed in derivative domain are integrated along the spectral axis and corrected for the accumulated errors brought by spectral integration. The algorithm was tested on airborne visible/infrared imaging spectrometer (AVIRIS) data cubes with signal-to-noise ratio (SNR) of 600 : 1. Experimental results show that the proposed algorithm can reduce the noise efficiently, and the SNR is improved to more than 2 000 : 1.

[Hyperspectral imagery denoising method based on wavelets].

To take advantage of the intrinsic characteristic of hyperspectral imageries, a hyperspectral imagery denoising method based on wavelet transform is proposed in the present paper. At first, two dimensional wavelet transform is performed on hyperspectral images band by band to capture their profiles. Due to the significant spectral correlation between adjacent bands, their high frequency wavelet coefficients are similar as well. Then, according to the wavelength relationship among the bands, which contain noise with different variances, new high frequency wavelet coefficients of seriously noisy bands are computed by the sum of weighted high frequency wavelet coefficients of bands, which contain low variance noise, and their profiles destroyed by noise are recovered in this way. Finally, the denoised images are reconstructed through inverse wavelet transform. The proposed method runs fast and can remove the noise efficiently. It was tested on airborne visible/infrared imaging spectrometer data (AVIRIS) cubes. Experimental results show that the signal-to-noise-ratio (SNR) of the reconstructed images in our method is 3.8-10.6 db higher than the that of the reconstructed images in the classical image denoising method, BayesShrink, and our method saves more than 50% computing time than BayesShrink method.