International Journal of Wavelets, Multiresolution and Information Processing

Fusion frame is a generalization of frame, which can analyze signals by projecting them onto multidimensional subspaces. Controlled fusion frame as generalization of fusion frame, it can improve the numerical efficiency of iterative algorithms for inverting the fusion frame operators. In this paper, we first introduce the notion of controlled g-fusion frame, discuss several properties of controlled g-fusion Bessel sequence. Then, we present some sufficient conditions and some characterizations of controlled g-fusion frames. Finally, we study the sum of controlled g-fusion frames.

This paper proposes a novel feature representation approach for heartbeat classification using single-lead electrocardiogram (ECG) signals based on adaptive Fourier decomposition (AFD). AFD is a recently developed signal processing tool that provides useful morphological features, which are referred as AFD-derived instantaneous frequency (IF) features and differ from those provided by traditional tools. The AFD-derived IF features, together with ECG landmark features and RR interval features, are trained by a support vector machine to perform the classification. The proposed method improves the average accuracy of the feature extraction-based methods, reaching a level comparable to deep learning but with less training data, and at the same time being interpretable for the learned features. It also greatly reduces the dimension of the feature set, which is a disadvantage of the feature extraction-based methods, especially for ECG signals. To evaluate the performance, the Association for the Advancement of Medical Instrumentation standard is applied to publicly available benchmark databases, including the MIT-BIH arrhythmia and MIT-BIH supraventricular arrhythmia databases, to classify heartbeats from the single-lead ECG. The overall performance is compared to selected state-of-the-art automatic heartbeat classification algorithms, including one-lead and even several two-lead-based methods. The proposed approach achieves superior balanced performance and real-time implementation.

The concept of Hilbert–Schmidt frame (HS-frame) was first introduced by Sadeghi and Arefijamaal in 2012. It is more general than $g$-frames, and thus, covers many generalizations of frames. This paper addresses the theory of HS-frames. We present a parametric and algebraic formula for all duals of an arbitrarily given HS-frame; prove that the canonical HS-dual induces a minimal-norm expression of the elements in Hilbert spaces; characterize when an HS-frame is an HS-Riesz basis, and when an HS-Bessel sequence is an HS-Riesz sequence (HS-Riesz basis) in terms of Gram matrices.

In this paper, we bound the errors of kernel regularized regressions associating with $2$-uniformly convex two-sided RKBSs and differentiable $\sigma (t)=\frac{|t{|}^p}{p}(1<p\le 2)$ uniformly smooth losses. In particular, we give learning rates for the learning algorithm with loss $V_p(t)=\frac{|t{|}^p}{p}(1<p\le 2)$. Also, we show a probability inequality and with which provide the error bounds for kernel regularized regression with loss $V_q(t)=\frac{|t{|}^q}{q}(q>2).$ The discussions are comprehensive applications of the uniformly smooth function theory, the uniformly convex function theory and uniformly convex space theory.

In this paper, comparison of common gate-common source single ended and differential ended Low Noise Amplifier (LNA) for Cognitive Radio (CR) receiver is presented. LNA for CR receiver architectures operating over a frequency range of 50–900MHz is designed for narrow band applications. In this work, Noise figure (NF), Third-Order Intercept Point (IIP3), voltage gain and scattering parameters (SP) have been analyzed. The voltage gain is 10.16866dB for single ended and 29.21371dB for differential ended, NF is 1.012dB for single ended and 3.8dB for differential ended. Power gain (S21) obtained is 15.67481dB for single ended and 14.89dB for differential ended. Compression point is $-5.62487$dB for single ended and $-5.32922$dB for differential ended, Third-Order Intercept Point (IIP3) is 1.97705 for single ended and 5.01608dB for differential ended amplifier, respectively. The design has been implemented using CMOS technology with cadence virtuoso design environment/automation tools.

We know that COVID-19 has been considered a pandemic and various types of symptoms are analyzed by the doctors. Various cases belonging to COVID-19 are asymptomatic and due to this fact the disease is not analyzed at an initial stage and the condition of the patient will be critical. So, the purpose of this work is to provide a solution that will find out the highly precise test result of COVID-19. Magnetic Resonance Imaging, CT Scan & Lung Ultrasound are some of the methods which can provide the exact results for the testing. But the problem associated with these imaging modalities is that they are time-consuming and the data provided by these modalities are large enough to store or transmit. A compression technique is required which can reduce the time as well as data size. Computed Tomography with Compressive Sensing (CS) Technique is used as an approach to tackle the above-stated problem. To analyze the fact that this technique is efficient, we consider the Computed Tomography-based Chest images of COVID-19 infected patients and apply the CS technique (Basis Pursuit) with Discrete Cosine Transform as a representation basis and Gaussian as a measurement matrix. As a result of this study, we find out three parameters, PSNR, SSIM & FSIM, to visualize the efficiency of the reconstruction strategy. This work concludes that the Computed Tomography approach with the help of CS can be used for fast and efficient imaging for COVID-19 as well as other diseases of the same kind.

This paper studies the binary classification problem associated with a family of Lipschitz convex loss functions called large-margin unified machines (LUMs), which offers a natural bridge between distribution-based likelihood approaches and margin-based approaches. LUMs can overcome the so-called data piling issue of support vector machine in the high-dimension and low-sample size setting, while their theoretical analysis from the perspective of learning theory is still lacking. In this paper, we establish some new comparison theorems for all LUM loss functions which play a key role in the error analysis of large-margin learning algorithms. Based on the obtained comparison theorems, we further derive learning rates for regularized LUMs schemes associated with varying Gaussian kernels, which maybe of independent interest.

Combining Matrix Factorization (MF) with Network Embedding (NE) has been a promising solution to social recommender systems. However, in most of the current combined schemes, the user-specific linking proportions learned by NE are fed to the downstream MF, but not reverse, which is sub-optimal as the rating information is not utilized to discover the linking features for users. Furthermore, the existing combined models mainly focus on enhancing the representation learning for users by exploiting user–user network, yet ignore the representation improvement for items. In this paper, we propose a novel social recommendation scheme, called MF with dual-network collaborative embedding (MF-decoding), which jointly optimizes an integrated objective function of MF and NE, in which both MF and NE tasks can be mutually reinforced in a unified learning process. In particular, the explicit user–user network and the implicit item–item network are collaboratively used by MF-decoding to enhance the representation learning for users and items simultaneously. Our encouraging experimental results on three benchmarks validate the superiority of the proposed MF-decoding model over state-of-the-art social recommendation methods.

Few studies have considered the information in the frequency domain to detect the structural breaks in financial markets. This paper provides a mixed model that integrates BEMD, AFD and Chow test to study the fluctuation characteristics of the soybean futures price. Due to the application of AFD, the mixed model can detect the structural breaks of the price fluctuation through obtaining the high-resolution information in the frequency domain. According to our results, in general, the soybean futures price in China is mainly determined by IMF11, followed by IMF9, IMF8 and IMF7, and there exist many structural breaks of different IMFs. Interestingly, national macro-controls have opposite effects at IMF8 and IMF11. The results show the effectiveness of the proposed mixed model for detecting structural breaks of financial markets in frequency-domain by revealing the impact of external events on the soybean futures price at multi-scales.

In this work, we give an introduction of uniform algebraic hyperbolic $B$-splines (UAH $B$-splines) generated over the space spanned by $\{sinh(\alpha x),cosh(\alpha x),\dots ,x^{k-3}sinh(\alpha x),x^{k-3}cosh(\alpha x)\}$, in which $k$ is an integer larger than or equal to $3$ and $\alpha$ is a tension parameter. Then, we construct a general formula of the refinement equation for any given order $k$ of these $B$-splines. Using the matrix version of this equation, we have also constructed the subdivision formula for UAH $B$-spline curves. In order to introduce a new reverse subdivision framework, entitled “Smooth Reverse Subdivision” associated with the cubic UAH $B$-splines, by continuing this process, we present a new multiresolution technique for general topology curves. We illustrate our results by numerical experiments.

In this paper, a novel discrete uncertainty principle associated with discrete Quaternion Fourier transform is established to give the relationship between the nonzero numbers of the discrete quaternion-valued signals and their Quaternion Fourier transforms. We obtain that the product of the numbers of nonzero elements of a sequence $f(t,s)$, $(t=0,1,\dots ,M-1,s=0,1,\dots ,N-1)$ and its Quaternion Fourier transform is no less than $MN$ and the result is sharp. Then we extend the uncertainty principle of discrete signals proved by Donoho and Starkin to two dimensional case. It suggests how sparsity helps in the recovery of missing frequency. The experimental results on the recovery of Lena also demonstrate the necessity of the two-dimensional discrete uncertainty principle associated with Quaternion Fourier transforms.

In this paper, we propose a sparse tensor regression model for multi-view feature selection. Apart from the most of existing methods, our model adopts a tensor structure to represent multi-view data, which aims to explore their underlying high-order correlations. Based on this tensor structure, our model can effectively select the meaningful feature set for each view. We also develop an iterative optimization algorithm to solve our model, together with analysis about the convergence and computational complexity. Experimental results on several popular multi-view data sets confirm the effectiveness of our model.