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A major key success factor regarding proficient Bayes threshold denoising refers to noise variance estimation. This paper focuses on assessing different noise variance estimations in three Bayes threshold models on two different characteristic brain lesions/tumor magnetic resonance imaging (MRIs).

Here, three Bayes threshold denoising models based on different noise variance estimations under the stationary wavelet transforms (SWT) domain are mainly assessed, compared to state-of-the-art non-local means (NLMs). Each of those three models, namely D1, GB and DR models, respectively, depends on the most detail wavelet subband at the first resolution level, on the entirely global detail subbands and on the detail subband in each direction/resolution. Explicit and implicit denoising performance are consecutively assessed by threshold denoising and segmentation identification results.

Implicit performance assessment points the first–second best accuracy, 0.9181 and 0.9048 Dice similarity coefficient (Dice), sequentially yielded by GB and DR; reliability is indicated by 45.66% Dice dropping of DR, compared against 53.38, 61.03 and 35.48% of D1 GB and NLMs, when increasing 0.2 to 0.9 noise level on brain lesions MRI. For brain tumor MRI under 0.2 noise level, it denotes the best accuracy of 0.9592 Dice, resulted by DR; however, 8.09% Dice dropping of DR, relative to 6.72%, 8.85 and 39.36% of D1, GB and NLMs is denoted. The lowest explicit and implicit denoising performances of NLMs are obviously pointed.

A future improvement of denoising performance possibly refers to creating a semi-supervised denoising conjunction model. Such model utilizes the denoised MRIs, resulted by DR and D1 thresholding model as uncorrupted image version along with the noisy MRIs, representing corrupted version ones during autoencoder training phase, to reconstruct the original clean image.

This paper should be of interest to readers in the areas of technologies of computing and information science, including data science and applications, computational health informatics, especially applied as a decision support tool for medical image processing.

In most cases, DR and D1 provide the first–second best implicit performances in terms of accuracy and reliability on both simulated, low-detail small-size region-of-interest (ROI) brain lesions and realistic, high-detail large-size ROI brain tumor MRIs.

An accurate long-term multi-step forecast provides crucial basic information for planning and reinforcing managerial decision-support. However, nonstationarity and nonlinearity, normally consisted of several types of managerial data can seriously ruin the forecasting computation. This paper aims to propose an effective long-term multi-step forecasting conjunction model, namely, wavelet–nonlinear autoregressive neural network (WNAR) conjunction model. The WNAR combines discrete wavelet transform (DWT) and nonlinear autoregressive neural network (NAR) to cope with such nonstationarity and nonlinearity within the managerial data; as a consequence, provides insight information that enhances accuracy and reliability of long-term multi-step perspective, leading to effective management decision-making.

Based on WNAR conjunction model, wavelet decomposition is executed for efficiently extracting hidden significant, temporal features contained in each of six benchmark nonstationary data sets from different managerial domains. Then, each extracted feature set at a particular resolution level is fed into NAR for the further forecast. Finally, NAR forecasting results are reconstructed. Forecasting performance measures throughout 1 to 30-time lags rely on mean absolute percentage error (MAPE), root mean square error (RMSE), Nash-Sutcliffe efficiency index or the coefficient of efficiency (E_f) and Diebold–Mariano (DM) test. An effect of data characteristic in terms of autocorrelation on forecasting performances of each data set are observed.

Long-term multi-step forecasting results show the best accuracy and high-reliability performance of the proposed WNAR conjunction model over some other efficient forecasting models including a single NAR model. This is confirmed by DM test, especially for the short-forecasting horizon. In addition, rather steady, effective long-term multi-step forecasting performances are yielded with slight effect from time lag changes especially for the data sets having particular high autocorrelation, relative against 95 per cent degree of confidence normal distribution bounds.

The WNAR, which combines DWT with NAR can be accounted as a bridge for the gap between machine learning, engineering signal processing and management decision-support systems. Thus, WNAR is referred to as a forecasting tool that provides insight long-term information for managerial practices. However, in practice, suitable exogenous input forecast factors are required on the managerial domain-by-domain basis to correctly foresee and effectively prepare necessary reasonable management activities.

Few works have been implemented to handle the nonstationarity, consisted of nonlinear managerial data to attain high-accurate long-term multi-step forecast. Combining DWT and NAR capabilities would comprehensively and specifically deal with the nonstationarity and nonlinearity difficulties at once. In addition, it is found that the proposed WNAR yields rather steady, effective long-term multi-step forecasting performance throughout specific long time lags regarding the data, having certainly high autocorrelation levels across such long time lags.

Accurate forecast of tourist arrivals is crucial for Thailand since the tourism industry is a major economic factor of the country. However, a nonstationarity, normally consisted in nonlinear tourism time series can seriously ruin the forecasting computation. The purpose of this paper is to propose a hybrid forecasting method, namely discrete wavelet decomposition (DWD)-NARX, which combines DWD and the nonlinear autoregressive neural network with exogenous input (NARX) to cope with such nonstationarity, as a consequence, improve the effectiveness of the demand-side management activities.

According to DWD-NARX, wavelet decomposition is executed for efficiently extracting the hidden significant, temporal features contained in the nonstationary time series. Then, each extracted feature set at a particular resolution level along with a relative price as an exogenous input factor are fed into NARX for further forecasting. Finally, the forecasting results are reconstructed. Forecasting performance measures rely on mean absolute percentage error, mean absolute error as well as mean square error. Model overfitting avoidance is also considered.

The results indicate the superiority of the DWD-NARX over other efficient related neural forecasters in the cases of high forecasting performance rate as well as competently coping with model overfitting.

The scope of this study is confined to Thailand tourist arrivals forecast based on short-term projection. To resolve such limitations, future research should aim to apply the generalization capability of DWD-NARX on other domains of managerial time series forecast under long-term projection environment. However, the exogenous input factor is to be empirically revised on domain-by-domain basis.

Few works have been implemented either to handle the nonstationarity, consisted in nonlinear, unpredictable time series, or to achieve great success on finding an appropriate and effective exogenous forecasting input. This study applies DWD to attain efficient feature extraction; then, utilizes the competent forecaster, NARX. This would comprehensively and specifically deal with the nonstationarity difficulties at once. In addition, this study finds the effectiveness of simply using a relative price, generated based on six top-ranked original tourist countries as an exogenous forecasting input.