Related papers: Non-decimated Quaternion Wavelet Spectral Tools wi…
We present a simple and effective approach for non-blind image deblurring, combining classical techniques and deep learning. In contrast to existing methods that deblur the image directly in the standard image space, we propose to perform…
This paper develops intrinsic wavelet denoising methods for surfaces of Hermitian positive definite matrices, with in mind the application to nonparametric estimation of the time-varying spectral matrix of a multivariate locally stationary…
A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with…
This paper presents a short evaluation about the integration of information derived from wavelet non-linear-time-invariant (non-LTI) projection properties using Support Vector Machines (SVM). These properties may give additional information…
It is well-known that a complex circulant matrix can be diagonalized by a discrete Fourier matrix with imaginary unit $\mathtt{i}$. The main aim of this paper is to demonstrate that a quaternion circulant matrix cannot be diagonalized by a…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
The bilateral filter is a useful nonlinear filter which without smoothing edges, it does spatial averaging. In the literature, the effectiveness of this method for image denoising is shown. In this paper, an extension of this method is…
In this work, we address the challenging problem of blind deconvolution for color images. Existing methods often convert color images to grayscale or process each color channel separately, which overlooking the relationships between color…
Transformations in the field of computer graphics and geometry are one of the most important concepts for efficient manipulation and control of objects in 2-dimensional and 3-dimensional space. Transformations take many forms each with…
Wavelet theory has been well studied in recent decades. Due to their appealing features such as sparse multiscale representation and fast algorithms, wavelets have enjoyed many tremendous successes in the areas of signal/image processing…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
In this paper we introduce and study the algebraic generalization of non commutative convolutional neural networks. We leverage the theory of algebraic signal processing to model convolutional non commutative architectures, and we derive…
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet…
Dual quaternion algebra and its application to robotics have gained considerable interest in the last two decades. Dual quaternions have great geometric appeal and easily capture physical phenomena inside an algebraic framework that is…
Non-cooperative communications using non-orthogonal multicarrier signals are challenging since self-created inter carrier interference (ICI) exists, which would prevent successful signal classification. Deep learning (DL) can deal with the…
In this study, we perform some analysis for the probability distributions in the space of frequency and time variables. However, in the domain of high frequencies, it behaves in such a way as the highly non-linear dynamics. The wavelet…
We present a novel framework for discrete multiresolution analysis of graph signals. The main analytical tool is the samplet transform, originally defined in the Euclidean framework as a discrete wavelet-like construction, tailored to the…
Quaternion-valued signal processing has received increasing attention recently. One key operation involved in derivation of all kinds of adaptive algorithms is the gradient operator. Although there have been some derivations of this…
Biomedical signal classification presents unique challenges due to long sequences, complex temporal dynamics, and multi-scale frequency patterns that are poorly captured by standard transformer architectures. We propose WaveFormer, a…