International Journal of Wavelets, Multiresolution and Information Processing

Dynamical sampling, as introduced by Aldroubi et al., deals with frame properties of sequences of the form ${\{T^{i-1}{f}_1\}}_{i\in \mathbb{N}}$, where $f_1$ belongs to Hilbert space ${\mathscr{H}}$ and $T:{\mathscr{H}}\to {\mathscr{H}}$ belongs to certain classes of bounded operators. Christensen et al. studied frames for ${\mathscr{H}}$ with index set $\mathbb{N}$ (or $\mathbb{Z}$), that has representations in the form ${\{T^{i-1}{f}_1\}}_{i\in \mathbb{N}}$ (or ${\{T^i{f}_0\}}_{i\in \mathbb{Z}}$). As frames of subspaces, fusion frames and generalized translation invariant systems are the special cases of $g$-frames, the purpose of this paper is to study and get sufficient conditions for $g$-frames $\mathrm{\Lambda }=\{{\mathrm{\Lambda }}_i\in B({\mathscr{H}},{𝒦}):i\in \mathbb{N}$ (or $\mathbb{Z})\}$ having the form ${\mathrm{\Lambda }}_{i+1}={\mathrm{\Lambda }}_1{T}^i,$ $T\in B({\mathscr{H}})$ (or ${\mathrm{\Lambda }}_{i+1}={\mathrm{\Lambda }}_0{T}^i,$ $T\in GL({\mathscr{H}})$). Also, we get the relation between representations of dual $g$-frames with index set $\mathbb{Z}$. Finally, we study stability of $g$-frame representations under some perturbations.

The radial basis functions meshfree method is a research method for thin plate problem which has gradually developed into a more mature meshfree method. It includes finite element, radial basis functions meshfree collocation method, etc. In this paper, we introduce the multilevel radial basis function collocation method for the fourth-order thin plate problem. We use nonsymmetric Kansa multilevel radial basis function collocation method to solve the fourth-order thin plate problem. Two numerical examples based on Wendland’s $C^6$ and $C^8$ functions are given to examine that the convergence of the multilevel radial basis function collocation method which is good for solving the fourth-order thin plate problem.

The main purpose of this paper is to introduce the notion of *-T-controlled frames in Hilbert $C^{*}$-modules. We present some results of frames in the view of *-T-controlled frames in Hilbert $C^{*}$-modules. Also, we define *-w-frames and give their relations to *-T-controlled frames and multiplier operators.

Artificial neural networks, consisting of many levels of nonlinearities, have been widely used to deal with various supervised learning tasks. At present, the most popular and effective training method is back-propagation algorithm (BP). Inspired by manifold regularization framework, we introduce a novel regularization framework, which aims at preserving the inter-object-distance of the data. Then a refined BP algorithm (IOD-BP) is proposed by imposing the proposed regularization framework into the objective function of BP algorithm. Comparative experiments on various benchmark classification tasks show that the new regularization BP method significantly improves the performance of BP algorithm in terms of classification accuracy.

Deep Learning in Traffic Sign Recognition (TSR) System is rapidly developing. Still, not much work has been reported in the literature on architectures that can work efficiently on multiple (more than two) databases across different countries. Each of these databases incorporates images of varied resolutions. Here, a Deep Neural Network called Multiple Database Efficient Network (MDEffNet) has been proposed for TSR. Batch normalization layers have been introduced to reduce the internal co-variant shift, and further, data augmentation has been carried out to achieve high efficiency with reasonable training time. Results at each step of the proposed architecture have been provided. The proposed model is compared with some state-of-the-art methods based on single or two databases, and solo works done in multiple (three) databases originating from different countries. The comparisons prove the high effectiveness of the proposed model. The achieved efficiency is much higher than all of them, including the average human ability. Deep learning techniques often suffer from increased memory and computational requirements. MDEffNet has only 1.36 million parameters ($\sim$ 26 times lower than the state-of-art methods) with 130 s per epoch, which is relatively low. Hence, it is also suitable for real-time embedded TSR systems.

Improved ant colony optimization (ACO) algorithms for continuous-domain optimization have been widely applied in recent years, but these improved methods have a weak perception of environmental information changes and only rely on the residues of the pheromones in the path to guide colony evolution. In this paper, we propose an ant colony algorithm based on the reinforcement learning model (RLACO). RLACO can acquire more environmental information by calculating the diversity of the ant colony, and, uses the diversity and other basic information of the ant colony to establish a reinforcement learning model. At different stages of evolution, the algorithm chooses an optimal strategy that can maximize the reward to improve the global search ability and convergence speed of the colony. The experimental results on CEC 2017 test functions show that the proposed algorithm is superior to other algorithms for continuous-domain optimization in convergence speed, accuracy and global search ability.

Since the introduction of R-duals by Casazza, Kutyniok and Lammers with the motivation to obtain a general version of duality principle in Gabor analysis, various R-duals and some relaxations of the R-dual setup have been introduced and studied by some mathematicians. They provide a powerful tool in the analysis of duality relations in general frame theory, and are far beyond the duality principle in Gabor analysis. In this paper, we introduce the concept of generalized weak R-dual based on a pair of frames which is a relaxation of the R-dual setup. Using generalized weak R-duals, we characterize the frame properties of a sequence and the equivalence between two frames, prove that the generalized weak R-duals of frames (Riesz bases) are frame sequences (frames), and present a coefficient expression corresponding to the canonical duals of generalized weak R-duals. Some examples are provided to illustrate the generality of the theory.

In the article, “Windowed special affine Fourier transform” in J. Pseudo-Differ. Oper. Appl. (2020), we introduced the notion of windowed special affine Fourier transform (WSAFT) as a ramification of the special affine Fourier transform. Keeping in view the fact that the WSAFT is not befitting for in the context of non-stationary signals, we continue our endeavor and introduce the notion of the special affine wavelet transform (SAWT) by combining the merits of the special affine Fourier and wavelet transforms. Besides studying the fundamental properties of the SAWT including orthogonality relation, inversion formula and range theorem, we also demonstrate that the SAWT admits the constant $Q$-property in the time–frequency domain. Moreover, we formulate an analog of the well-known Poisson summation formula for the proposed SAWT.

Bank NIFTY index prediction is a challenging problem, which dictates that the market is highly stochastic, and there are temporally dependent predictions from chaotic data. Thus, the development of an effective prediction model is required as the basic necessity and in this paper, the Bank NIFTY index prediction system is developed using the Deep Convolutional Long Short-Term Memory (Deep-ConvLSTM) model that effectively predicts the Bank NIFTY index. The overall procedure of the proposed approach involves three steps. The initial step is feature extraction, the second step is clustering, and the tertiary step is the prediction. The input data is fed to the feature extraction step. Here, the feature extraction is performed based on the technical indicators, and then the clustering is done based on modified Sparse Fuzzy $C$-Means (FCM) in order to find the effective features. Finally, the prediction is carried out based on Deep-ConvLSTM model, which is trained optimally using the proposed Adaptive-Rider-Monarch Butterfly Optimization (Adaptive-Rider-MBO) for performing accurate prediction. The performance of the Bank NIFTY index prediction based on Adaptive-Rider-MBO is evaluated based on Mean Square Error (MSE) and Root Mean Square Error (RMSE). The proposed method achieves the minimal MSE of 2.010 and minimal RMSE of 1.418 based on the NIFTY Midcap 100 index.

Computer-based diagnostics of schizophrenia (SZ) have been recently the subject of intense interest. Some recent studies have shown promising results in the diagnosis of this disorder by the process and analysis of neuroimaging data, such as functional magnetic resonance imaging (fMRI), structural magnetic resonance imaging (sMRI) and diffusion tensor imaging (DTI). Each of these neuroimaging data provides different brain structural and functional features that integrating them can help accurately diagnose brain disorders. In this study, we propose a deep learning architecture to combine functional brain data with two different types of structural brain data to accurately diagnose SZ. Our two-step model consists of deep belief networks (DBN) and a fusing rule to extract and learn hidden features via the combining resting-state fMRI with both sMRI and DTI data. We examine this architecture on all combinations of features extracted from fMRI, MRI and DTI. The experimental results indicate that multi-modal fusion improved classification accuracy between the SZ and the healthy cases. By finding a suitable configuration for algorithm parameters, the proposed method showed an accuracy level of 99.36% for the COBRE dataset and outperformed similar state-of-the-art works.

In this paper, we derive the Cramer–Rao lower bound (CRLB) in a non-additive white Gaussian noise (AWGN) model for the affine phase retrieval (APR) and simulate the difference of CRLB and mean square error produced by PhaseLift of phase retrieval and APR in AWGN and non-AWGN cases.

In this study, we develop a generalized wavelet-based collocation method to solve the fractional Pennes bioheat transfer model during hyperthermia treatment. Unlike the existing operational matrix methods based on orthogonal functions, we formulate the Haar wavelet operational matrices of general order integration without using the block pulse functions. Consequently, the governing problem is transformed into an equivalent system of algebraic equations, which can be tackled with any classical method. Some prime features of the proposed method include no requirement of the inverse of the Haar matrices, no need to convert the boundary value problem into the initial-value problem, which in turn eliminates the possibility of unstable solutions. The proposed technique is testified for different values of fractional parameter $\alpha$ and is observed that as the fractional parameter $\alpha$ increases, the tissue temperature at the target region also increases appreciably. Moreover, the obtained results also indicate that the overall time taken to attain the hyperthermia temperature for the fractional model is comparatively less than the classical bioheat model.