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Nonlinear diffusion has been proved to be an indispensable approach for the removal of noise in image processing. In this paper, we employ nonlinear diffusion for the purpose of denoising audio signals in order to have this approach also recognized as a powerful tool for audio signal processing. We apply nonlinear diffusion to wavelet coefficients obtained from different filters associated with orthogonal and biorthogonal wavelets. We use wavelet decomposition to keep signal components well-localized in time. We compare denoising results using nonlinear diffusion with wavelet shrinkage for different wavelet filters. Our experiments and results show that the denoising is much improved by using the nonlinear diffusion process. [ABSTRACT FROM AUTHOR]

Partial Discharge (PD) measurements of large generators are extremely affected and hampered by noise, making the denoising of PD signal an inevitable issue. Wavelet shrinkage is the most commonly employed method for PD signal denoising. The appropriate mother wavelet and decomposition level are critically important for the denoising performance. In consideration of the PD signal characteristics of large generators, a novel wavelet shrinkage scheme for PD signal denoising is presented. In the scheme, a scale dependent wavelet selection method is proposed; the core idea is that the optimum wavelet at each scale is selected as the one maximizing the energy ratio of coefficients beside and inside the range formed by the threshold, which correspond to the signal to be reserved and noise to be removed, respectively. In addition, taking into account the influence of mother wavelet at each scale on the decomposition level, an approach for decomposition level determination is put forward based on the energy composition after decomposition at each scale. The application results on the simulated signals with different SNR obtained by combining the various pulses and measured signal on-site show the effectiveness of the proposed scheme. Besides, the denoising results are compared with that of the existing wavelet selection methods and the proposed wavelet selection method shows an obvious advantage. [ABSTRACT FROM AUTHOR]

An interferometric synthetic aperture radar (InSAR) phase denoising algorithm using the local sparsity of wavelet coefficients and nonlocal similarity of grouped blocks was developed. From the Bayesian perspective, the double- l1 norm regularization model that enforces the local and nonlocal sparsity constraints was used. Taking advantages of coefficients of the nonlocal similarity between group blocks for the wavelet shrinkage, the proposed algorithm effectively filtered the phase noise. Applying the method to simulated and acquired InSAR data, we obtained satisfactory results. In comparison, the algorithm outperformed several widely-used InSAR phase denoising approaches in terms of the number of residues, root-mean-square errors and other edge preservation indexes. [ABSTRACT FROM AUTHOR]

Background subtraction without a separate training phase has become a critical task, because a sufficiently long and clean training sequence is usually unavailable, and people generally thirst for immediate detection results from the first frame of a video. Without a training phase, we propose a background subtraction method based on three-dimensional (3D) discrete wavelet transform (DWT). Static backgrounds with few variations along the time axis are characterized by intensity temporal consistency in the 3D space-time domain and, hence, correspond to low-frequency components in the 3D frequency domain. Enlightened by this, we eliminate low-frequency components that correspond to static backgrounds using the 3D DWT in order to extract moving objects. Owing to the multiscale analysis property of the 3D DWT, the elimination of low-frequency components in sub-bands of the 3D DWT is equivalent to performing a pyramidal 3D filter. This 3D filter brings advantages to our method in reserving the inner parts of detected objects and reducing the ringing around object boundaries. Moreover, we make use of wavelet shrinkage to remove disturbance of intensity temporal consistency and introduce an adaptive threshold based on the entropy of the histogram to obtain optimal detection results. Experimental results show that our method works effectively in situations lacking training opportunities and outperforms several popular techniques. [ABSTRACT FROM AUTHOR]

Background subtraction without a separate training phase has become a critical task, because a sufficiently long and clean training sequence is usually unavailable, and people generally thirst for immediate detection results from the first frame of a video. Without a training phase, we propose a background subtraction method based on three-dimensional (3D) discrete wavelet transform (DWT). Static backgrounds with few variations along the time axis are characterized by intensity temporal consistency in the 3D space-time domain and, hence, correspond to low-frequency components in the 3D frequency domain. Enlightened by this, we eliminate low-frequency components that correspond to static backgrounds using the 3D DWT in order to extract moving objects. Owing to the multiscale analysis property of the 3D DWT, the elimination of low-frequency components in sub-bands of the 3D DWT is equivalent to performing a pyramidal 3D filter. This 3D filter brings advantages to our method in reserving the inner parts of detected objects and reducing the ringing around object boundaries. Moreover, we make use of wavelet shrinkage to remove disturbance of intensity temporal consistency and introduce an adaptive threshold based on the entropy of the histogram to obtain optimal detection results. Experimental results show that our method works effectively in situations lacking training opportunities and outperforms several popular techniques.