Design of Speech Denoising Algorithm Based on Wavelet Threshold Function and PSO

At present, there are many shortcomings in the discontinuity of wavelet threshold function and the constant threshold of different decomposition layers and the constant error it produced. The amplitude-frequency characteristics of wavelet filters are studied and analyzed by mathematical modeling. An improved wavelet threshold function with adjustable parameters is proposed. Particle swarm optimization (PSO) algorithm is used to find the optimal parameters of the improved threshold function in a background noise environment. The improved wavelet threshold function is combined with Bayesian threshold method to obtain the threshold based on Bayesian criterion, which makes the threshold adaptive in different layers and overcomes the shortcomings of fixed threshold. Finally, the speech signal with optimal wavelet coefficients is obtained after reconstruction. Compared with the traditional threshold function, Simulation results show that the improved threshold function achieves precise notch denoising, effectively retains the singularity and eigenvalues of the signal, and reduces the signal distortion.

-NONUNIFORM MULTIRESOLUTION ANALYSIS

Gabardo and Nashed [‘Nonuniform multiresolution analyses and spectral pairs’, J. Funct. Anal.158(1) (1998), 209–241] have introduced the concept of nonuniform multiresolution analysis (NUMRA), based on the theory of spectral pairs, in which the associated translated set $\Lambda =\{0,{r}/{N}\}+2\mathbb Z$ is not necessarily a discrete subgroup of $\mathbb{R}$ , and the translation factor is $2\textrm{N}$ . Here r is an odd integer with $1\leq r\leq 2N-1$ such that r and N are relatively prime. The nonuniform wavelets associated with NUMRA can be used in signal processing, sampling theory, speech recognition and various other areas, where instead of integer shifts nonuniform shifts are needed. In order to further generalize this useful NUMRA, we consider the set $\widetilde {\Lambda }=\{0,{r_1}/{N},{r_2}/{N},\ldots ,{r_q}/{N}\}+s\mathbb Z$ , where s is an even integer, $q\in \mathbb {N}$ , $r_i$ is an integer such that $1\leq r_i\leq sN-1,\,(r_i,N)=1$ for all i and $N\geq 2$ . In this paper, we prove that the concept of NUMRA with the translation set $\widetilde {\Lambda }$ is possible only if $\widetilde {\Lambda }$ is of the form $\{0,{r}/{N}\}+s\mathbb Z$ . Next we introduce $\Lambda _s$ -nonuniform multiresolution analysis ( $\Lambda _s$ -NUMRA) for which the translation set is $\Lambda _s=\{0,{r}/{N}\}+s\mathbb Z$ and the dilation factor is $sN$ , where s is an even integer. Also, we characterize the scaling functions associated with $\Lambda _s$ -NUMRA and we give necessary and sufficient conditions for wavelet filters associated with $\Lambda _s$ -NUMRA.

Hybrid of the Lee-Carter Model with Maximum Overlap Discrete Wavelet Transform Filters in Forecasting Mortality Rates

This study implements various, maximum overlap, discrete wavelet transform filters to model and forecast the time-dependent mortality index of the Lee-Carter model. The choice of appropriate wavelet filters is essential in effectively capturing the dynamics in a period. This cannot be accomplished by using the ARIMA model alone. In this paper, the ARIMA model is enhanced with the integration of various maximal overlap discrete wavelet transform filters such as the least asymmetric, best-localized, and Coiflet filters. These models are then applied to the mortality data of Australia, England, France, Japan, and USA. The accuracy of the projecting log of death rates of the MODWT-ARIMA model with the aforementioned wavelet filters are assessed using mean absolute error, mean absolute percentage error, and mean absolute scaled error. The MODWT-ARIMA (5,1,0) model with the BL14 filter gives the best fit to the log of death rates data for males, females, and total population, for all five countries studied. Implementing the MODWT leads towards improvement in the performance of the standard framework of the LC model in forecasting mortality rates.

Modelling Price Volatility in Onion using Wavelet based Hybrid Models

The performance of wavelet-based hybrid models using different combinations of wavelet filters was compared to that of other conventional models to model volatility in the onion prices and arrivals at the Lasalgaon market of Maharashtra, which is known to be one of the largest markets in terms of arrivals. Monthly data of more than twenty-three years from 1996 onwards were taken into account. The results of hybrid models were compared to that of the ARIMA model. A normality test was conducted for both data series, and both of them were found to be non-normal. Therefore, a suitable nonparametric approach, namely wavelet decomposition of the data, was called for. For the price data, too, the wavelet- GARCH model with LA8 filter at five-level decomposition performed best for single value forecast, whereas the ARIMA performed well at expanded horizons. For the arrivals data, the Wavelet-GARCH model with LA8 filter at four level decomposition outperformed all models for single value forecasts. However, the wavelet-ANN model was able to perform better as the horizon expanded to twelve months. The study concluded that the wavelet hybrid models do pretty well for single value forecast, but as the horizon expands, the accuracy of the models decreases.

Machine learning-based CT radiomics features for the prediction of pulmonary metastasis in osteosarcoma

Objective: This study aims to build machine learning-based CT radiomic features to predict patients developing metastasis after osteosarcoma diagnosis. Methods and materials: This retrospective study has included 81 patients with a histopathological diagnosis of osteosarcoma. The entire dataset was divided randomly into training (60%) and test sets (40%). A data augmentation technique for the minority class was performed in the training set, along with feature’s selection and model’s training. The radiomic features were extracted from CT’s image of the local osteosarcoma. Three frequently-used machine-learning models tried to predict patients with lung metastasis (MT) and those without lung metastasis (non-MT). According to the higher area under the curve (AUC), the best classifier was chosen and applied in the testing set with unseen data to provide an unbiased evaluation of the final model. Results: The best classifier for predicting MT and non-MT groups used a Random Forest algorithm. The AUC and accuracy results of the test set were bulky. (accuracy of 73% [ 95% coefficient interval (CI): 54%; 87%] and AUC of 0.79 [95% CI: 0.62; 0.96]). Features that fitted the model (radiomics signature) derived from Laplacian of Gaussian and wavelet filters. Conclusions: Machine learning-based CT radiomics approach can provide a non-invasive method with a fair predictive accuracy of the risk of developing pulmonary metastasis in osteosarcoma patients. Advances in knowledge: Models based on CT radiomic analysis help assess the risk of developing pulmonary metastases in patients with osteosarcoma, allowing further studies for those with a worse prognosis.