International Journal of Wavelets, Multiresolution and Information Processing

In this paper, we defined Calder$\acute{\text{o}}$n–Zygmund operator $T$ as $(T\varphi )(x)={\int }_{𝕂}\mathcal{𝒦}(x,y)\varphi (y)dy$ on local fields ($𝕂$) under certain conditions on $\mathcal{𝒦}(x,y)$ and then find the boundedness of operator $T$. Using result on boundedness of $T$ and orthonormal wavelet basis of $L^2(𝕂)$, we provide unconditional wavelet bases for $L^p$-norm over a local fields of positive characteristic by the wavelet coefficients.

Desynchronization attacks proved to be the greatest challenge to audio watermarking systems as they introduce misalignment between the signal carrier and the watermark. This paper proposes a DNN-based speech watermarking system with two adversarial networks jointly trained on a set of desynchronization attacks to embed a randomly generated watermark. The detector neural network is expanded with spatial pyramid pooling layers to be able to handle signals affected by these attacks. A detailed training procedure of the aforementioned DNN system with gradual attack introduction is proposed in order to achieve robustness. Experiments performed on a speech dataset show that the system achieves satisfactory results according to all the benchmarks it was tested against. The system preserves signal quality after watermark embedding. Most importantly, the system achieved resistance to all considered desynchronization attacks. The majority of the attacks cause less than $1.70$% of incorrectly detected watermarked bits on average, which outperforms comparative techniques in this regard.

Hyperspectral image (HSI) classification methods based on deep learning have demonstrated excellent performance, while these deep learning methods take a lot of time to train the parameters. In this paper, we propose a deep sparse representation (SR) network (DSRNet) without spending a lot of time training network parameters in the feature extraction stage. The contributions of this paper are three-fold. First, we introduce random dictionary into HSI classification, and solve sparse representation model under this dictionary. Second, we extend the shallow sparse representation model to the deep sparse representation model, where the SR model needs to be solved for each layer and used to extract the deep features of HSI. Finally, we investigate the classification performance of different classifiers on the deep features extracted by using DSRNet. Experimental results show that the proposed method can achieve better classification results compared with some closely related HSI classification methods and the other state-of-the-art deep learning methods.

In this paper, we propose an applicable algorithm of the so-called adaptive Fourier decomposition in $H^2({ℂ}^{+})$ the Hardy $H^2$ space on the upper half-plane ${ℂ}^{+}$, which provides a new method for decomposing real-valued signals and analytic signals on the real line. As a by-product, a new approach for computing the Hilbert transform on the real line is also given. Numerical experiments are used to demonstrate the performance of the proposed algorithm.

Anomaly detection in public places using the video surveillance gains significance due to the real-time monitoring and security that ensures the personal assets and public security. Accordingly, in this research, a deep CNN model with Timber–Prairie wolf optimization algorithm (TPWO) optimization is proposed for surveillance-based anomaly detection. To support the TPWO-based deep CNN anomaly detection model, tracking model named OptSpatio tracking model tracks the location and movement of the anomalous objects in any locality. The OptSpatio tracking model uses both visual and spatial tracking models to monitor any anomalous activity. On the other hand, TPWO is designed to tune the deep classifier for acquiring better detection performance. The TPWO-based model surpasses the competent methods in terms of accuracy by 97.214%, sensitivity by 97.831% and specificity by 96.668% with minimal EER of 2.786%. The MOTP values are also obtained at a rate of 0.7325; moreover, the effectiveness of the TPWO method is justified at the object-, frame-, and pixel-level analysis.

A new version of ambiguity function (AF) associated with the offset linear canonical transform (OLCT) is considered in this paper. This new version of AF coined as the $k$-AF associated with the OLCT ($k$-AFOL) is defined based on the OLCT and the fractional instantaneous auto-correlation. A natural magnification effect characterized by the extra degrees of freedom of the OLCT and by a factor $k$ on the frequency axis enables the $k$-AFOL to have flexibility to be used in cross-term reduction. Firstly, we defined the $k$-AF associated with the OLCT ($k$-AFOL), and establish its relationship with the $k$-Wigner distribution in OLCT domain. Later on, we define the basic properties including the scaling, conjugate-symmetry, shifting, marginal and Moyal’s formulae of $k$-AFOL in depth. The results show that $k$-AFOL can be viewed as one of the generalizations of the classical AF which has elegance, simplicity and flexibility in the frequency marginal property. The novelty of our paper lies in applications part, where we have shown how the proposed transform is used for the detection of single-component and bi-component linear frequency-modulated (LFM) signals.

Let $v_1,v_2$ be vertices of a graph $G$ with degree of the vertices being $d(v_1)$ and $d(v_2),$ respectively. First, let us define the weight of the edge $v_1{v}_2$ as twice the value of $\frac{1}{d(v_1)+d(v_2)}$ in $G$. Let us define $H(G)$, the harmonic index of the graph $G$, as the sum obtained by adding the weight assigned to every edge of $G$. In this paper, for the class of trees, we shall obtain an upper bound for the harmonic index $H(G)$ in terms of the edge-vertex domination number and the order of $G$. Also, we shall ascertain that the equality is true by characterizing the collection of all extremal trees attaining this bound.

The phase retrieval (PR) problem is to reconstruct real/complex functions from the magnitudes of their Fourier/frame measurements in classical computational imaging. In this paper, we consider phase retrieval of complex vectors/images from the magnitudes of short-time fractional Fourier transform (STFrFT). In our setting, the above problem is solved by minimizing a least square ReLu loss function and a novel algorithm by alternating direction method of multipliers (ADMM) is presented. As shown in the numerical simulations on complex signals/images, our proposed PR-ADMM algorithm from STFrFT has a better recovery performance with flexible window functions and appropriate fractional orders. It demonstrates to have satisfactory performance from mixed phaseless STFrFT measurements. Compared with several six other main algorithms, the proposed algorithm explicitly recovers the phase of image with higher the peak signal-to-noise ratio. Meanwhile, the proposed algorithm is robust to noise. These also generalize some of about phase retrievals with Fourier measurements.

In this paper, we propose a method to realize single image super resolution using a network composed of residual blocks with a cross architecture and wavelet transform. For the high quality of the reconstructed high resolution image, the brightness change must be sharp at the edge and gentle at the flat region. In single image super resolution, it is important to accurately predict the high-frequency components of the image. Hence, we propose a method to realize single image super resolution by estimating the high-frequency component in the wavelet domain using neural network composed of residual blocks with two crossing skip connections.

Tremendous efficient optimization methods have been proposed for strongly convex objectives optimization in modern machine learning. For non-strongly convex objectives, a popular approach is to apply a reduction from non-strongly convex to a strongly convex case via regularization techniques. Reduction on objectives with adaptive decrease on regularization tightens the optimal convergence of algorithms to be independent on logarithm factor. However, the initialization of parameter of regularization has a great impact on the performance of the reduction. In this paper, we propose an aggressive reduction to reduce the complexity of optimization for non-strongly convex objectives, and our reduction eliminates the impact of the initialization of parameter on the convergent performances of algorithms. Aggressive reduction not only adaptively decreases the regularization parameter, but also modifies regularization term as the distance between current point and the approximate minimizer. Our aggressive reduction can also shave off the non-optimal logarithm term theoretically, and make the convergent performance of algorithm more compact practically. Experimental results on logistic regression and image deblurring confirm this success in practice.