International Journal of Wavelets, Multiresolution and Information Processing

In standard U-net, researchers only use long skip connections to skip features from the encoding path to the decoding path in order to recover spatial information loss during downsampling. However, it would result in gradient vanishing and limit the depth of the network. To address this issue, we propose a novel deep fully residual convolutional neural network that combines the U-net with the ResNet for medical image segmentation. By applying short skip connections, this new extension of U-net decreases the amount of parameters compared to the standard U-net, although the depth of the layer is increased. We evaluate the performance of the proposed model and other state-of-the-art models on the Electron Microscopy (EM) images dataset and the Computed Tomography (CT) images dataset. The result shows that our model achieves competitive accuracy on the EM benchmark without any further post-process. Moreover, the performance of image segmentation on CT images of the lungs is improved in contrast to the standard U-net.

We consider the $1$d and $2$d bicomplex analogues of the classical Fourier–Wigner transform. Their basic properties, including Moyal’s identity and characterization of their ranges giving rise to new bicomplex–polyanalytic functional spaces are discussed. Details concerning a special window function are developed explicitly. An orthogonal basis for the space of bicomplex-valued square integrable functions on the bicomplex numbers is constructed by means of a specific class of bicomplex Hermite functions.

Frame multiresolution analysis (FMRA) in $L^2(ℝ)$ is an important topic in frame theory and its applications. In this paper, we consider the so-called multiscaling FMRA in $L^2({ℝ}^n)$, which has matrix dilations and a finite number of scaling functions. This framework is a generalization of the theories both on monoscaling FMRA and on the classical MRA of multiplicity $d$. We characterize wavelet frames and Parseval wavelet frames for $L^2({ℝ}^n)$ under the circumstances that they can be associated with a multiscaling FMRA. We give two necessary and sufficient conditions for given functions ${\{{\psi }_k\}}_{k=1}^K$ in $V_1$ to be multiframe generators of $W_0=V_1\ominus V_0$. Especially, the second condition depends on the multiscaling FMRA and ${\{{\psi }_k\}}_{k=1}^K$ only, does not require the existence of other functions, and is relatively easier to verify. Moreover, for any finitely-generated frame of integer translates, we give explicitly the Fourier transforms of the generators of its canonical dual frame. We illustrate the implementation and an application of the theory with an example.

Chart patterns are one of the important tools used by the financial analysts for predicting future price trends (subsequent trends) in stock markets. Although many works related to the descriptions of chart patterns and several effective methods to identify chart patterns from the financial time series have been proposed in recent years, there is no in-depth study about the general characteristics of the subsequent trends. In this paper, we proposed a general framework for mining subsequent trend for chart patterns. We extensively analyze the characteristics of subsequent trends of chart patterns found with the proposed framework. Based on the analysis, we propose a concept called subsequent trend pattern by mining frequently occurring shapes from these trends. The process of subsequent trend pattern mining was evaluated on a dataset containing 502 time series from S&P 500 and a test dataset containing 494 stocks from Yahoo finance. The proposed concept of subsequent trend pattern provides a solid foundation for the understanding of chart patterns in predicting future price movement and extends the formal definition of chart patterns.

The shape of local window plays a vital role in the estimation of original signal variance, which is used to shrink the noisy wavelet coefficients in wavelet-based image denoising algorithms. This paper presents an anisotropic-shaped region-based Wiener filtering (ASRWF) and BayesShrink (ASRBS) algorithms, which exploit the region characteristics to estimate the original signal variance using a statistical approach. The proposed approach divides the region centered on a noisy wavelet coefficient into various non-overlapping subregions. The Euclidean distance-based measure is considered to obtain the similarities between reference subregion and adjacent subregions. An appropriate threshold value is estimated by applying a statistical approach on these distances and the sets of similar and dissimilar subregions are obtained from a defined region. Thus, an anisotropic-shaped region is obtained by neglecting the dissimilar subregions in a defined region. The variance of every similar subregion is calculated and then averaged to estimate the original signal variance to shrink noisy wavelet coefficients effectively. Finally, the estimated signal variance is utilized in Wiener filtering and BayesShrink algorithms to improve the denoising performance. The performance of the proposed algorithms is analyzed qualitatively and quantitatively on standard images for different noise levels.

Automatic aircraft engine defect detection is a challenging but important task in industry which can ensure safe air transportation and flight. In this paper, we propose a fast and accurate feature weighting network (FWNet) to solve the problem of defect scale variation and improve detection accuracy. The framework is designed based on recent popular convolutional neural networks and feature pyramid. To further boost the representation power of the network, a new feature weighting module (FWM) was proposed to recalibrate the channel-wise attention and increase the weights of valid features. The model was trained and tested on a self-built dataset, which consisted of 1916 images and contained three defect types: ablation, crack and coating missing. Extensive experimental results verify the effectiveness of the proposed FWM and show that the proposed method can accurately detect engine defects of different scales and different locations. Our method obtains 89.4% mAP and can run at 6FPS, which surpasses other state-of-the-art detection methods and can quickly provide diagnostic basis for aircraft maintenance inspectors in practical applications.

In this paper, we study nonuniform average sampling problem in multiply generated shift-invariant subspaces of mixed Lebesgue spaces. We discuss two types of average sampled values: average sampled values $\{〈f,{\psi }_a(\cdot -x_j,\cdot -y_k)〉:j,k\in 𝕁\}$ generated by single averaging function and average sampled values $\{〈f,{\psi }_{x_j,y_k}〉:j,k\in 𝕁\}$ generated by multiple averaging functions. Two fast reconstruction algorithms for these two types of average sampled values are provided.

Traditional supervised dimensionality reduction methods can establish a better model often under the premise of a large number of samples. However, in real-world applications where labeled data are scarce, traditional methods tend to perform poorly because of overfitting. In such cases, unlabeled samples could be useful in improving the performance. In this paper, we propose a semi-supervised dimensionality reduction method by using partial least squares (PLS) which we call semi-supervised partial least squares (S2PLS). To combine the labeled and unlabeled samples into a S2PLS model, we first apply the PLS algorithm to unsupervised dimensionality reduction. Then, the final S2PLS model is established by ensembling the supervised PLS model and the unsupervised PLS model which using the basic idea of principal model analysis (PMA) method. Compared with unsupervised or supervised dimensionality reduction algorithms, S2PLS not only can improve the prediction accuracy of the samples but also enhance the generalization ability of the model. Meanwhile, it can obtain better results even there are only a few or no labeled samples. Experimental results on five UCI data sets also confirmed the above properties of S2PLS algorithm.

In this paper, we first introduce uncertainty principles for the quaternion Fourier transform (QFT). We then provide a different proof of the well-known properties of the quaternionic windowed Fourier transform (QWFT) using properties of the QFT which is a little bit simpler than usual. Based on uncertainty principles for the QFT and the relationship between the QFT and QWFT, we establish uncertainty principles related to the QWFT.

This paper considers wavelet estimation for density derivatives based on negatively associated and size-biased data. We provide upper bounds of nonlinear wavelet estimator on $L^p(1\le p<\infty )$ risk. It turns out that the convergence rate of the nonlinear estimator is better than that of the linear one.

A generalization of the multivariate Strang–Fix conditions to no scale-invariant (only shift-invariant) polynomial spaces multiplied by exponents is introduced. A method to construct nonstationary compactly supported interpolating scaling functions that the scaling functions reproduce polynomials multiplied by exponents is presented. The polynomials (multiplied by exponents) are solutions to systems of linear constant coefficient PDEs, where the symbols of the differential operators that define PDEs can be no scale-invariant and can contain constant terms. Analytically calculated graphs of the scaling functions, including nonstationary, are presented. A concept of the so-called $N$-separate MRAs is considered; and it is shown that, in the case of isotropic dilation matrices, the $N$-separate scaling functions appear naturally.

In this paper, a cascadic Newton’s method is designed to solve the Monge–Ampère equation. In the process of implementing the cascadic multigrid, we use the Full-Local type interpolation as prolongation operator and Newton iteration as smoother. In order to obtain Full-Local type interpolation, we provide several finite difference stencils. Especially, the skewed finite difference methods are first applied by us for the elliptic Monge–Ampère equation. Based on Full-Local interpolation techniques and cascade principle, the new algorithm can save a large amount of computation time. Some numerical experiments are provided to confirm the efficiency of our proposed method.