International Journal of Wavelets, Multiresolution and Information Processing

In this paper, we develop a collocation method for solving three-dimensional partial differential equations using Haar wavelet and Kronecker tensor product. The approach is based on a series of Haar wavelet basis functions to approximate sixth-order mixed derivatives. The proposed method is mathematically fast, less error and straightforward for the numerical solution of many types of three-dimensional Poisson, biharmonic and Helmholtz equations. Some numerical examples verify the accuracy and efficiency of the proposed method. Finally, we conclude that numerical results computed by our proposed method are more accurate than numerical results obtained in the existing methods in the literature. We find that the CPU time consumed by the suggested approach is lesser than the CPU time of existing methods. Thus, the process is fast, efficient and has a low numerical error.

Traditional wavelet frame packets are based on square iterative matrices and frame scaling functions. Since the Fourier transform of frame scaling functions are discontinuous, the resulting wavelet frame packets do not possess time-frequency localization. In this study, we will develop the new construction of wavelet frame packets by using non-square iterative matrices: one is to construct wavelet frame packets directly from known non-GMRA wavelet frames to obtain finer time-frequency structure, the other is based on GMRA wavelet frames constructed from smooth generalization scaling functions, the corresponding quasi-projection formula and fast algorithm are also given.

In this paper, we consider the Plancherel formula for Fourier integral operator on the space $L^2({ℍ}^2)$, where $ℍ$ is the quaternion skew field. By using the metaplectic representations of a noncompact classical dual pair $(S{O}^{\ast }(4),Sp(1,1))$ and combining with the Plancherel formula of Poisson transform, we obtain the direct integral decomposition of all irreducible unitary representations of Fourier integral operator.

The enormous amount of data contained in the video image has grown rapidly along with surveillance, greatly outpacing the capacity of human resources to handle it effectively. Smart surveillance retrieval is an essential component of any modern video surveillance system, considerably boosting the effectiveness, precision, and interoperability of the system. The use of face recognition and other cutting-edge technology in the security surveillance system is rapidly rising. Therefore, in this article, the distributed deep convolutional neural network (DCNN) and distributed deep BiLSTM is proposed to efficiently detect the face from the video. One of the major contributions involved in this research relies on the key frame selection, where four unique distance measurement techniques are fused, and is named hybrid distance- key frame selection. The Tri birds optimization (TBO) technique selects the best solution from a large number of solutions for the ensemble model classifier engaged in face recognition. The ensemble model classifier incorporates various hyper-parameters that are optimally trained. Multiple test videos with 401 and 802 test videos are used as the input for the TBO-ensemble model that attains 97% accuracy, 98.33% precision, recall, and f-measure for epoch 50 and the 500 number of retrievals, respectively.

Lower bound estimation plays an important role for establishing the minimax risk. A key step in lower bound estimation is deriving a lower bound of the affinity between two probability measures. This paper provides a simple method to estimate the affinity between mixture probability measures. Then we apply the lower bound of the affinity to establish the minimax lower bound for a family of sparse covariance matrices, which contains Cai–Ren–Zhou’s theorem in [T. Cai, Z. Ren and H. Zhou, Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation, Electron. J. Stat. 10(1) (2016) 1–59] as a special example.

Variable selection is one of the most important contents of machine learning research and a large number of variable selection methods have been proposed at present. From deep learning perspective, we propose a new variable selection method based on multi-layer artificial neural networks in this paper. The method propagates errors gained form a trained network model through the network from output layer to input layer and the values gained by input layer give information about the relative contribution. The variables with big contribution value are selected, which we call neural inverse propagation (NIP). Specifically, after training a neural network, the gained errors between the actual network outputs and the desired outputs go through the network from top to down and arrive at the input layer. The absolute values gained by input units provide information about the relative importance (contribution) of input units, which is that the larger the value is, the more important the corresponding input variable is. We remove k variables corresponding to the first k minimum absolute value gained by input units to the predictive variables, to perform variable selection. The efficiency of the proposed method is illustrated through its application to classification and regression tasks on a number of synthetic datasets and a real-world image classification dataset.

Due to the advantages of direct visualization and high resolution, transmission electron microscopy (TEM) technology has been widely used in the morphological identification of viruses. With the development of artificial intelligence (AI), there have been some studies on automated TEM virus identification using deep learning. However, to achieve effective virus identification results, a large number of high-quality labeled images are required for network training. In this work, we propose an automatic virus segmentation method based on few-shot learning. We use the Chikungunya virus, Parapoxvirus and Marburg virus, etc. to construct a pre-training virus dataset and train an attention U-Net-like network with an encoder module, relationship module, attention module and decoding module to realize severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2) segmentation using few-shot learning. The experiment shows that the proposed few-shot learning methods yield 0.900 Dice and 0.828 Jaccard in 1-shot, 0.903 Dice and 0.832 Jaccard in 5-shot, which demonstrates the effectiveness of our method and outperforms other promising methods. Our fully automated method contributes to the development of medical virology by providing virologists with a low-cost and accurate approach to identify SARS-CoV-2 in TEM.

In real scenarios, objects with high aspect ratios are actually very common, and such objects hold significant importance in the field of object detection. However, most of the existing object detection algorithms tend to overlook this specific type of object. After analyzing the statistical data, we observed a substantial decrease in mAP (mean Average Precision) for classical object detection algorithms when they are tasked with detecting only high aspect ratio objects. Therefore, we conducted an analysis of the factors that influence the detection performance of these objects and made the following improvements: (1) We introduced large-kernel attention convolution between the backbone network layers. This addition allows each position feature to have a larger receptive field, facilitating better feature learning; (2) By incorporating multiple sets of deformable convolutions for feature-adaptive processing, we were able to enhance the learning of characteristic information specific to the object itself. This approach also promotes network convergence. The proposed method yielded a significant improvement in accuracy, approximately 5$\%$ higher than the baseline, when evaluated on the FGSD2021 dataset. Furthermore, our method outperformed the current best method by approximately 0.5$\%$.

The fractional Fourier transform (FRFT) is a generalized form of the Fourier transform (FT), it is another important class of time–frequency analysis tool in signal processing. In this paper, we study the two-dimensional (2D) FRFT in the polar coordinates setting. First, Parseval theorem of the 2D FRFT in the polar coordinates is obtained. Then, according to the relationship between 2D FRFT and fractional Hankel transform (FRHT), the convolution theorem for the 2D FRFT in polar coordinates is obtained. It shows that the FRFT of the convolution of two functions is the product of their respective FRFTs. Moreover, the fast algorithm for the convolution theorem of the 2D FRFT is discussed. Finally, the sampling theorem for signal is explored.

Objectives:This research presents an approach to detect occluded face images. In order to achieve this, the research presents a novel technique that involves feature extraction and occluded face recognition.

Methods: Feature extraction is performed by the enhanced ORB algorithm, which is proposed by the modification of the Oriented Fast and Rotated Brief (ORB) algorithm, by adding a phase for contrast adjustment, together with CNN features. For occluded face recognition, a Generative Adversarial Network (GAN) optimized by the proposed SR-SSA is designed. SR-SSA is proposed by the integration of Search and Rescue Optimization (SAR) in the Sparrow Search Algorithm (SSA).

Results: The experimental results demonstrate that the SR-SSA-based GAN algorithm outperforms existing methods in terms of accuracy of 0.956, FAR of 0.045 and FRR of 0.021.