International Journal of Wavelets, Multiresolution and Information Processing

In today’s scientific epoch, speech is an important means of communication. Speech enhancement is necessary for increasing the quality of speech. However, the presence of noise signals can corrupt speech signals. Thereby, this work intends to propose a new speech enhancement framework that includes (a) training phase and (b) testing phase. The input signal is first given to STFT-based noise estimate and NMF-based spectra estimate during the training phase in order to compute the noise spectra and signal spectra, respectively. The obtained signal spectra and noise spectra are then Wiener-filtered, then empirical mean decomposition (EMD) is used. Because the tuning factor of Wiener filters is so important, it should be computed for each signal by coaching in a fuzzy wavelet neural network (FW-NN). Subsequently, a bark frequency is computed from the denoised signal, which is then subjected to FW-NN to identify the suitable tuning factor for all input signals in the Wiener filter. For optimal tuning of $\eta$, this work deploys the fitness-oriented elephant herding optimization (FO-EHO) algorithm. Additionally, an adaptive Wiener filter is used to supply EMD with the ideal tuning factor from FW-NN, producing an improved speech signal. At last, the presented approach’s supremacy is proved with varied metrics.

In this paper, we introduce the notion of quaternion linear canonical S-transform (Q-LCST) which is an extension of the linear canonical S-transform and study the uncertainty principles associated with the Q-LCST. First, we propose the definition of Q-LCST and then study the fundamental properties of $Q$-LCST including linearity, shift, modulation, orthogonality relation and reconstruction formula. Second, we derive the associated Heisenbergs uncertainty inequality and the corresponding logarithmic version for $Q$-LCST. Finally, some potential applications of the Q-LCST are introduced.

Due to ${\mathrm{ℝ}}_{+}$ not being a group under addition, $L^2({\mathrm{ℝ}}_{+})$ admits no traditional wavelet or Gabor frame. This paper addresses a class of dilation-and-modulation (${ℳ}{𝒟}$) Parseval frames for $L^2({\mathrm{ℝ}}_{+})$. We present a parametric expression of all ${ℳ}{𝒟}$-Parseval frames (frame sequences) and ${ℳ}{𝒟}$-orthonormal bases (systems); and develop an approach to obtain all ${ℳ}{𝒟}$-Parseval frames (frame sequences) and ${ℳ}{𝒟}$-orthonormal bases (systems) starting with one ${ℳ}{𝒟}$-Parseval frame for $L^2({\mathrm{ℝ}}_{+})$.

Due to the ongoing research in the medical domain, we get lot of data for storage and transmission purposes. Real-time processing and reduction of medical data are tedious. Hence, an approach is required to compress the data and reconstruct it by using a few samples. We proposed a model with a remote Health Care Unit & Patient for EEG signals in this work. In this model, our prime concern is to reduce the number of samples to reconstruct a compressed EEG signal. So, to reduce the number of samples, we opt for compressive sensing approach. As it is a well-known concept, Compressive Sensing is the framework that mainly depends upon the Sensing matrix for compression and the Basis matrix for representation. By considering this fact, we demonstrate a technique, which is a combination of the Compressive Sensing and BSBL by employing different measurement matrices. Since BSBL has already been mentioned in the literature, we compared the results based on this demonstration with the previously mentioned approach and found a significant change in the parameters mentioned in the result and analysis section.

We study the reconstruction of multidimensional digital signals in multirate digital signal processing. We show that the composition of sampling operator and interpolation operator forms the frame operator of multivariate discrete time wavelet (MDTW) system of scale matrix ${𝒩}$. By taking a collection of $M$ filters, we construct dual MDTW tight frames. Also, we discuss the existence and construction of MDTW Parseval frames in multidimensional sequence space. The necessary and sufficient condition for the existence of orthonormal basis of scale matrix ${𝒩}$ is discussed. Using dual MDTW tight frame, we characterize biorthogonal pair of Riesz bases. Further, we define multivariate Parseval frame of weighted exponentials, dual multivariate tight frame of weighted exponentials of scale matrix ${𝒩}$ in periodic space ${\text{L}}^2([0,1{)}^d)$. Finally, we give the applications of MDTW frames in the theory of frames of weighted exponentials of scale matrix ${𝒩}$ in periodic space ${\text{L}}^2([0,1{)}^d)$.

In this paper, a special group is used to introduce the two-direction two-scale similarity transform (TDTST) of the two-direction refinable function, and the existence of the solution of the two-direction refinable equation is discussed by the TDTST transform. The approximation order of the two-direction refinable function is discussed by the TDTST transform. Whether the TDTST transform can maintain the orthogonality of the two-direction refinable function is discussed, and it is pointed out that a special real orthogonal matrix can maintain the orthogonality. It is pointed out that the TDTST transform can maintain the symmetry of the two-direction refinable function. Finally, an example is given.

In this paper, we will present several new results in finite and countable dimensional separable real Hilbert space phase retrieval and norm retrieval by fusion frames. We will characterize of norm retrieval for fusion frames similar norm retrieval for vectors and we will show that only one direction holds for fusion frames. In similar vector case, we will show that every tight fusion frame can do norm retrieval. Also we will show that the unitary operators preserve phase (norm) retrievability of fusion frames. We will make a detailed study of when hyperplanes do norm retrieval and show a general result about it. We will provide numerous examples to show that our results are best possible.

Non-negative matrix factorization (NMF) is a powerful tool for image data analysis and has been utilized in a range of applications involving data classification, clustering, and image processing. Nevertheless, NMF and most of its variants are unsupervised learning algorithms and do not take account of the projection property of the basis image matrix. These flaws will have a negative impact on their classification performance. To resolve the mentioned drawbacks of NMF-based methods, this paper establishes a novel projective non-negative matrix factorization (PNMF) framework using the class-label information and deals with the model via a bi-level quadratic optimization (BLO) strategy. The convergence of the proposed BLO-PNMF algorithm is theoretically analyzed and proved in detail, and also verified by experiments. Our approach and the related state-of-the-art methods are evaluated and compared on three face databases. The experimental results indicate that the BLO-PNMF method can extract more localized features for image data representation and achieve superior performance in face recognition.

Distributed learning is a very effective divide-and-conquer strategy for dealing with big data. As distributed learning algorithms become more and more mature, network security issues including the risk of privacy disclosure of personal sensitive data, have attracted high attention and vigilance. Differentially private is an important method that maximizes the accuracy of a data query while minimizing the chance of identifying its records when querying from the given data. The known differentially private distributed learning algorithms are based on variable perturbation, but the variable perturbation method may be non-convergence and the experimental results usually have large deviations. Therefore, in this paper, we consider differentially private distributed learning algorithm based on objective function perturbation. We first propose a new distributed logistic regression algorithm based on objective function perturbation (DLR-OFP). We prove that the proposed DLR-OFP satisfies differentially private, and obtain its fast convergence rate by introducing a new acceleration factor for the gradient descent method. The numerical experiments based on benchmark data show that the proposed DLR-OFP algorithm has fast convergence rate and better privacy protection ability.

In Blind Hyperspectral Unmixing, the accuracy of the estimated number of endmembers affects the succeeding steps of extraction of endmember signatures and acquiring their fractional abundances. The characteristics of endmember signature depend on the nature of the material on the ground and share similar characteristics for variants of the same material. In this paper, we introduce a new concept of sub-endmembers to identify similar materials that are variants of a global endmember. Identifying the sub-endmembers will provide a meaningful interpretation of the endmember variability along with increased unmixing accuracy. This paper proposes a new algorithm exploiting both the spatial and spectral information present in hyperspectral data. The hyperspectral data are segmented into homogenous regions (superpixels) based on the Simple Linear Iterative Clustering (SLIC) algorithm, and the mean spectral of each region is accounted for in finding the global endmembers. The difference of eigenvalues-based thresholding method is used to find the number of global and sub-endmembers. The method has been tested on synthetic and real hyperspectral data and has successfully estimated the number of global endmembers as well as sub-endmembers. The method is also compared with other state-of-the-art methods, and better performances are obtained at a reasonably lower computational complexity.