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In this paper, a robust and efficient digital image watermarking algorithm using the fast Hadamard transform (FHT) is proposed for the copyright protection of digital images. This algorithm can embed or hide an entire image or pattem as a watermark such as a company's logo or trademark directly into the original image. The performance of the proposed algorithm is proof of rightful ownership. Over the past few years, the technology of digital watermarking has gained prominence and emerged as a leading candidate that could solve the fundamental problems of legal ownership and content authentications for digital multimedia data (e.g. audio, image, and video).

The vibration signals of wind turbines are often disturbed by strong noise and will be annihilated when exhibiting fault or strong instability. Denoising is required prior to facilitating an analysis of vibration fault characteristics. A wavelet denoising method based on variational mode decomposition (VMD) and multiscale permutation entropy (MPE) is proposed. The characteristics of VMD are analyzed, and the randomness and complexity of noise are evaluated by MPE. If the MPE of the modal component after VMD is larger than the evaluation value, then it is denoised by wavelet, and the signal is reconstructed with other modal components without wavelet denoising to achieve the denoising effect. The db1, sym8, EMD and EWT denoising methods and the proposed method are compared using the same simulation signal. Simulation results show that the denoising effect of the proposed method is better than the other four methods, and the two quantitative evaluation indexes of relative error and root mean square error obtain desirable values. The shaft vibration signals of the Case Western Reserve University and wind turbine are used to verify the effectiveness of the proposed method, and the denoising effect is also better than the other four methods. The proposed method eliminates most of the noise components while retaining the effective information of the signal. Therefore, this method can provide a good foundation for the research and analysis of the characteristics of late vibration signal.

In this paper, we analyze some properties of the orthogonal Gaussian-Hermite moments and propose a new method to detect the moving objects using the orthogonal Gaussian-Hermite moments. For the segmentation of moving objects in such moment images, we propose the fuzzy relaxation method (FRM) and 3D morphological relaxation method (3DMRM). The experiment results are reported, which show the robustness of our methods.