International Journal of Wavelets, Multiresolution and Information Processing

This note designs two kinds of rational wavelet filter banks using three basic bricks: the finite Blaschke product, Bezout polynomial and the symbol of the cardinal B-spline. In orthogonal case, the corresponding wavelets are generalization of Daubechies’ wavelets. The role of the Blaschke product is the adjustment of the peaks of wavelet functions.

A gene is a basic unit of congenital traits and a sequence of nucleotides in deoxyribonucleic acid that encrypts protein synthesis. Proteins are made up of amino acid residue and are classified for use in protein-related research, which includes identifying changes in genes, finding associations with diseases and phenotypes, and identifying potential drug targets. To this end, proteins are studied and classified, based on the family. For family prediction, however, a computational rather than an experimental approach is introduced, owing to the time involved in the latter process. Computational approaches to protein family prediction involve two important processes, feature selection and classification. Existing approaches to protein family prediction are alignment-based and alignment-free. The drawback of the former is that it searches for protein signatures by aligning every available sequence. Consequently, the latter alignment-free approach is taken for study, given that it only needs sequence-based features to predict the protein family and is far more efficient than the former. Nevertheless, the sequence-based characteristics taken for study have additional features to offer. There is, thus, a need to select the best features of all. When comes to classification still there is no perfection in classifying the protein. So, a comparison of different approaches is done to find the best feature selection technique and classification technique for protein family prediction. From the study, the feature subset selected provides the best classification accuracy of 96% for filter-based feature selection technique and the random forest classifier.

Image inpainting is the process to fill missing pixels in the damaged image and this process has drawn more attraction and gained active and expensive research topic in recent decades, because the high quality in the image inpainting benefits a greater range of applications, like object removal, photo restoration, and so on. Inpainting of larger quality of the image needs to fill the empty regions with plausible content in the damaged image. The existing inpainting methods either fill image regions by stealing the image patches or semantically create coherent patches from the regional context. Most of the traditional models perform well on small holes images, but restoring the image with large holes still results a challenging task. To overcome such issues and to generate effective inpainting results, a proposed method named the hybrid context deep learning approach is designed in order to fill empty regions of crack images. Moreover, the proposed method is more effective by employing a hybrid optimization algorithm for training of classifier to generate a more robust and accurate inpainted result. The developed model includes two different deep learning classifiers to accomplish the process of image inpainting in such a way that the results are fused through the probabilistic model. Moreover, the proposed approach attains higher performance by the metrics such as Peak signal-to-noise ratio (PSNR), Structural Similarity Index (SSIM), Second Derivative like Measure of Enhancement (SDME), and Universal Quality Index (UQI) with the values of 38.02db, 0.867, 54.32db, and 0.864, respectively.

The deformable derivative [${𝒟𝒟}$] is used in this work to give the necessary restrictions for the existence of mild solutions for perturbed fractional neutral differential equations [PFNDE] in Banach spaces. Several novel existence results are made using fixed point and semigroup techniques. In the end, two numerical examples are given to illustrate the application of the theoretical concepts discussed.

Refinable functions play an important role in the construction and properties of wavelets. Basically, most of the wavelets are generated from refinable functions. In this paper, a study on the approximation properties of refinable functions on $p$-adic fields is carried out with necessary theoretical background. Various equivalent forms of approximation order and the connection between the approximation order and the Strang–Fix condition are derived. Finally a characterization for the approximation order of a refinable function is given in terms of order of the sum rules associated with the refinement mask.

The outbreak of the global COVID-19 pandemic has become a public crisis and is threatening human life in every country. Recently, researchers have developed testing methods via patients cough recordings. In order to improve the testing accuracy, in this paper, we establish a novel COVID-19 sound-based diagnosis framework, i.e. TFA-CLSTMNN, which integrates time-frequency domain features of the recorded cough with the Attention-Convolution Long Short-Term Memory Neural Network. Specifically, we calculate the Mel-frequency cepstrum coefficient (MFCC) of the cough data to extract the time-frequency domain features. We then apply the convolutional neural network and the attentional mechanism on the time-frequency features, which is followed by the long short-term memory neural network to analyze the MFCC features of the data. The recognition and classification can be then carried out to evaluate the positiveness or negativeness of the tested samples. Experimental results show that the proposed TFA-CLSTMNN framework outperforms the baseline neural networks in sound-based COVID-19 diagnosis and derives an accuracy over 0.95 on the public real-world datasets.

Principal component analysis (PCA) may be the most popular dimension reduction method. In this paper, the learning scheme of kernel PCA methods is established. Moreover, for the uncentered case, we introduce the error representation, and prove the comparison theorem that the learning error can be bounded by the excess generalization error. Under the condition that the positive eigenvalues of $L_K$ are all single, the satisfied error bound $O(n^{-\frac{1}{2}})$ is deduced.