Related papers: Non-decimated Quaternion Wavelet Spectral Tools wi…

Some connections between operator theory and wavelet analysis: Since the mid eighties, it has become clear that key tools in wavelet analysis rely crucially on operator theory. While isolated variations of wavelets, and wavelet…

Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…

In this paper we propose a new adaptive wavelet denoising methodology using complex wavelets. The method is based on a fully Bayesian hierarchical model in the complex wavelet domain that uses a bivariate mixture prior on the wavelet…

This paper introduces a meta-learning approach for parameterized pseudo-differential operators with deep neural networks. With the help of the nonstandard wavelet form, the pseudo-differential operators can be approximated in a compressed…

Dense pixelwise prediction such as semantic segmentation is an up-to-date challenge for deep convolutional neural networks (CNNs). Many state-of-the-art approaches either tackle the loss of high-resolution information due to pooling in the…

Utilizing complex-valued neural networks (CVNNs) in wireless communication tasks has received growing attention for their ability to provide natural and effective representation of complex-valued signals and data. However, existing studies…

In real life application all signals are not obtained from uniform shifts; so there is a natural question regarding analysis and decompositions of these types of signals by a stable mathematical tool. Gabardo and Nashed and Gabardo and Yu…

This article introduces quaternion non-negative matrix factorization (QNMF), which generalizes the usual non-negative matrix factorization (NMF) to the case of polarized signals. Polarization information is represented by Stokes parameters,…

Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called…

Wavelet neural network (WNN), which learns an unknown nonlinear mapping from the data, has been widely used in signal processing, and time-series analysis. However, challenges in constructing accurate wavelet bases and high computational…

In this paper, we introduce the notion of quaternion shearlet transform- which is an extension of the ordinary shearlet transform. Firstly, we study the fundamental properties of quaternion shearlet transforms and then establish some basic…

In this paper novel classes of 2-D vector-valued spatial domain wavelets are defined, and their properties given. The wavelets are 2-D generalizations of 1-D analytic wavelets, developed from the Generalized Cauchy-Riemann equations and…

Deploying deep neural networks on edge devices is often limited by the memory traffic and compute cost of dense linear operators. While quaternion neural networks improve parameter efficiency by coupling multiple channels through Hamilton…

In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in [1], and it is defined via a hierarchical…

In this paper, the inverse problem of reconstructing reflectivity function of a medium is examined within a blind deconvolution framework. The ultrasound pulse is estimated using higher-order statistics, and Wiener filter is used to obtain…

Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in…

The field of neural networks has seen significant advances in recent years with the development of deep and convolutional neural networks. Although many of the current works address real-valued models, recent studies reveal that neural…

A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…

Employing ideas of noncommutative geometry, certain dimensional invariant for quantum homogeneous spaces has been proposed and here we take up its computation for quaternion spheres.

We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the…