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Diaphragmatic electromyography (EMGdi) signals can effectively reflect human respiratory process and effort, but simultaneously interfered by electrocardiogram (ECG) signals, leading to the limited application of EMGdi signals. Conventional denoising schemes for ECG cancellation from EMGdi signals are usually limited to the cases of irregular ECG signals. For this purpose, this paper proposes a denoising method of ECG signals by using a dual-threshold filter, which performs effectively in the scenarios of irregular ECG condition, such as arrhythmia. Specifically, we first employ wavelet transform to decompose EMGdi signals to wavelets of different frequencies, by which QRS complex detection is performed to determine the location of ECG signals. Then we propose to remove the ECG interference by reforming the interference range with the adjacent signals. Experimental results indicate that the proposed denoising method performs superior to the state-of-the-art schemes, especially for the cases of weak EMGdi signal scenarios.

Statistical modeling of wavelet coefficients is a critical issue in wavelet domain signal processing. By analyzing the defects of other existing methods, and exploiting the local dependency of wavelet coefficients, an efficient statistical model is proposed. Improved variance estimation of the local wavelet coefficients can be obtained using the new model. Then we apply an approximate minimum mean squared error (MMSE) estimation procedure to restore the wavelet image coefficients. The modeling process is computational cost saving, and the denoising experiments show the algorithm outperforms other approaches in peak-signal-to-noise ratio (PSNR).

Currently, the wavelet transform is widely used in the signal processing domain, especially in the image compression because of its excellent de-correlation property and the redundancy property included in the wavelet coefficients. This paper investigates the redundancy relationships between any two or three components of the wavelet coefficients, the wavelet bases and the original signal. We discuss those contents for every condition according to the continuous form and the discrete form, respectively, by which we also derive a uniform formula which illuminates the inherent connection among the redundancy of the wavelet coefficients, the wavelet bases and the original signals. Finally, we present the application of the wavelet coefficient redundancy property in the still image compression domain and compare the properties of the Discrete Wavelet Transform (DWT) with that of the Discrete Cosine Transform (DCT).

The earthquake shows certain characteristics of periodicity or quasi-periodicity, which has been constantly proved by facts and these characteristics have been widely used in analyzing the trend of the seismic activities. On the basis of wavelet analysis, the seismic data in southwest from 1900 to 2013 was analyzed and the features on different time scales were studied. Moreover, an analysis of the future seismic trend was conducted by using wavelet coefficients on all scales and the main period of seismic activities.

Image denoising is a significant procedure in image processing, and a good denoising method can improve the image quality. This study focuses on enhancing the estimation model of wavelet coefficients by improving the threshold function. Thus, a general construction method for a class of threshold functions is introduced, and sufficient conditions are given to ensure that the threshold functions are continuous, first-order differentiable and higher-order differentiable. It makes an existing class of improved threshold functions a particular case and enables the construction of other needed threshold functions based on this general approach. Experiments have shown that using the new threshold functions yields better denoising results for images containing salt and pepper noise, Gaussian noise and speckle noise. Moreover, as the smoothness of the threshold function is enhanced, the denoising effect is also improved. The improved wavelet coefficients estimation model can effectively boost the quality of image denoising, further enhancing the accuracy and effectiveness of computer vision algorithms.

In this paper, emphasis is placed on de-noising via thresholding, which is based on wavelet transform. This paper also analyses the characteristic of signal and noise by wavelet transform, de-noising method by Donoho and other's improving scheme. According to the feature of noise and the continuity of signal, the improvement schemes are put forward on dealing with the preprocessing procedure to signal observation. These schemes are uncomplicated and practical.

Under noise situations, the wavelet coefficient of noise may affect the recognition and character extraction of linear frequency modulation (LFM) signal, especially the condition of S/N (signal-noise-ratio) is lower. The wavelet transform of Gaussian noise and LFM signal is firstly analyzed. Because the modulus maximum value of wavelet coefficient of noise is reduced when increasing the scale, while its amplitude keeps invariable, we propose an adaptive-threshold method, which use the difference of wavelet coefficient between the noise and LFM signal to denoise. This method denotes a threshold according to N/S, when the wavelet coefficient is lower than the threshold, noise can be filtered. For LFM signal, so far as its frequency can bestrew the whole intermediate frequency of the receiver, then according to wavelet coefficient and its space between modulus maximum value, the LFM carrier frequency can be extracted effectively.

This paper integrated the advantages of co-occurrence matrix and wavelet transform and proposed a new method based on wavelet coefficient co-occurrence matrix. The new approach constructed four co-occurrence matrices based on wavelet coefficient matrix, and then it picked up the texture parameters of the four co-occurrence matrices for image retrieval, it not only considered the spatial correlation info, but also took full advantage of excellent character of wavelet transform. The experimental results show that the new method has an advanced general performance and its computational complexity is lower than wavelet histogram technology.