International Journal of Wavelets, Multiresolution and Information Processing

Scaling and generalized scaling sets determine wavelet sets and hence wavelets. In real case, wavelet sets were proved to be an important tool for the construction of MRA as well as non-MRA wavelets. However, any result related to scaling/generalized scaling sets is not available in case of locally compact abelian groups. This paper gives a characterization of scaling sets and its generalized version along with relevant examples in dual Cantor dyadic group $G^{\ast }$. These results can further be generalized to arbitrary locally compact abelian groups.

In this paper, we investigate the wavelet-based estimators of a kind of censored mixture density and discuss their pointwise asymptotic convergence rates over Hölder spaces. We first consider the linear wavelet estimator and give its upper bound. However, the linear one is nonadaptive and not applicable since it is related to the unknown space parameter. Finally, we use the hard threshold method to explore adaptive nonlinear wavelet estimator and obtain the same convergence order as the linear one up to a logarithmic penalty.

This paper gives a kind of sharp simultaneous approximation error estimation of Birkhoff interpolation $\text{for all }1\le p,q\le \infty ,0\le s\le r-1$,

In this paper, we prove that the unconditional constants of the g-frame expansion in a Hilbert space are bounded by $\sqrt{B/A}$, where $A$, $B$ are the frame bounds of the g-frames. It follows that tight g-frames have unconditional constant one. Then we generalize this to a classification of such g-frames by showing that a g-Bessel sequence has unconditional constant one if it is an orthogonal sum of g-tight frames. We also obtain a new result under which a g-Bessel sequence is a g-frame from the view of unconditional constant. Finally, we prove similar results for cross g-frame expansions as long as the cross g-frame expansions stay uniformly bounded away from zero.

We study the Kolmogorov and the linear approximation numbers of the Besov classes ${MB}_{p,𝜃}^{\mathrm{\Omega }}$ with mixed smoothness in the norm of $L_q$ in the randomized setting. We first establish two discretization theorems. Then based on them, we determine the exact asymptotic orders of the Kolmogorov and the linear approximation numbers for certain values of the parameters $p,q,𝜃$. Our results show that the linear randomized methods lead to considerably better rates than those of the deterministic ones for $2\le p\le q<\infty$.

This paper considers wavelet estimations of a regression function based on negatively associated sample. We provide upper bound estimations over $L^p(1\le p<\infty )$ risk of linear and nonlinear wavelet estimators in Besov space, respectively. When the random sample reduces to the independent case, our convergence rates coincide with the optimal convergence rates of classical nonparametric regression estimation.

Image fusion is an important concept in remote sensing. Earth observation satellites provide both high-resolution panchromatic and low-resolution multispectral images. Pansharpening is aimed on fusion of a low-resolution multispectral image with a high-resolution panchromatic image. Because of this fusion, a multispectral image with high spatial and spectral resolution is generated. This paper reports a new method to improve spatial resolution of the final multispectral image. The reported work proposes an image fusion method using wavelet packet transform (WPT) and principal component analysis (PCA) methods based on the textures of the panchromatic image. Initially, adaptive PCA (APCA) is applied to both multispectral and panchromatic images. Consequently, WPT is used to decompose the first principal component of multispectral and panchromatic images. Using WPT, high frequency details of both panchromatic and multispectral images are extracted. In areas with similar texture, extracted spatial details from the panchromatic image are injected into the multispectral image. Experimental results show that the proposed method can provide promising results in fusing multispectral images with high-spatial resolution panchromatic image. Moreover, results show that the proposed method can successfully improve spectral features of the multispectral image.

Speckle suppression and elimination are very important to improve the visual quality of ultrasound image and the diagnostic ability of the diseases. An effective technique of image denoising based on discrete wavelet transform is to employ a Bayesian maximum a posteriori (MAP) estimator. To suppress and remove the speckle noise using MAP estimator effectively, it must assign correctly the shrinkage function based on appropriate probability density functions (PDFs) for the wavelet coefficients of logarithmically transformed noise-free ultrasound image and speckle noise. In this paper, we introduce a new closed-form shrinkage function that is an analytical solution of a Bayesian MAP estimator for despeckling of the ultrasound images effectively in wavelet domain. We employ a Cauchy prior and Gaussian PDF to model the wavelet coefficients of logarithmically transformed noise-free ultrasound image and speckle noise, respectively. Firstly, we derive the CauchyShrinkGMAP that is a closed-form shrinkage function. In addition, we estimate the noise variance and parameter of MAP estimator. Next, we evaluate the despeckling performance of wavelet image denoising method using the CauchyShrinkGMAP compared to various despeckling method using median and Wiener filters, hard and soft thresholding and GaussShrinkGMAP and MCMAP3N shrinkage function. The experiment results show that PSNR of new closed-form shrinkage function is highest, MSE is smallest, and the correlation coefficient ($\rho$) and SSIM are closer to one than the other existing image denoising methods for noisy synthetic ultrasound images at different speckle noise levels. Also, experiment results show that ENL of new closed-form shrinkage function is highest and that of EN and SD is smallest than the other existing image denoising methods for noisy real ultrasound image.

People communicate their views, arguments and emotions about their everyday life on social media (SM) platforms (e.g. Twitter and Facebook). Twitter stands as an international micro-blogging service that features a brief message called tweets. Freestyle writing, incorrect grammar, typographical errors and abbreviations are some noises that occur in the text. Sentiment analysis (SA) centered on a tweet posted by the user, and also opinion mining (OM) of the customers review is another famous research topic. The texts are gathered from users’ tweets by means of OM and automatic-SA centered on ternary classifications, namely positive, neutral and negative. It is very challenging for the researchers to ascertain sentiments as a result of its limited size, misspells, unstructured nature, abbreviations and slangs for Twitter data. This paper, with the aid of the Gradient Boosted Decision Tree classifier (GBDT), proposes an efficient SA and Sentiment Classification (SC) of Twitter data. Initially, the twitter data undergoes pre-processing. Next, the pre-processed data is processed using HDFS MapReduce. Now, the features are extracted from the processed data, and then efficient features are selected using the Improved Elephant Herd Optimization (I-EHO) technique. Now, score values are calculated for each of those chosen features and given to the classifier. At last, the GBDT classifier classifies the data as negative, positive, or neutral. Experiential results are analyzed and contrasted with the other conventional techniques to show the highest performance of the proposed method.

Massive multiple-input multiple-output (MIMO) is an emerging technology used in next-generation cellular networks. The major challenge in the massive MIMO system is the pilot contamination. The contamination of the pilot sequences causes inaccurate channel estimation leading to huge errors in the transmissions. This paper proposes an approach for pilot contamination reduction in massive MIMO systems. In order to reduce the pilot contamination, a pilot scheduling algorithm is devised by proposing an optimization algorithm named Elephant-based Spider Monkey Optimization (ESMO) for scheduling the pilots. The proposed ESMO is designed by combining Elephant Herding Optimization (EHO) into Spider Monkey Optimization (SMO). The pilot scheduling approach employs proposed ESMO and user degradation for scheduling the pilots. Moreover, the optimal pilot scheduling is carried out using the newly devised fitness function that considers achievable rate using various user grouping parameters, such as utility function, and grouping parameter. Thus, the proposed ESMO-based pilot scheduling and fitness function are responsible for initiating optimal pilot scheduling. The performance of the proposed method is compared with the existing methods, and the proposed ESMO outperformed the existing methods with maximal achievable rate value of 39.257bps/Hz, and maximal SINR with value 118.75dB, respectively.

In this paper, a construction of three interval frame scaling sets is described and certain classes of normalized tight frame wavelet sets are also constructed with the help of these three interval frame scaling sets. We also generalize this construction to obtain $n$-interval frame scaling sets.

The objective of this paper is to give a study on Bézier and B-Spline curves. The paper has divided into three parts. The first studies Bézier curves and their mathematical solutions, while the second describes B-spline curves and their mathematical solutions. Finally, the application of B-spline curves in wavelet decomposition is shown. The PeakSignal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) are considered for evaluation, and it is justified that Bézier and B-spline curves are indispensable in the field of computer graphics.