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Surface-consistent deconvolution is a standard processing technique in land data to uniformize the wavelet across all sources and receivers. The required wavelet estimation step is generally done in the homomorphic domain since this is a…
A Deep Belief Network (DBN) requires large, multiple hidden layers with high number of hidden units to learn good features from the raw pixels of large images. This implies more training time as well as computational complexity. By…
The Number Theoretic Transform (NTT) can be regarded as a variant of the Discrete Fourier Transform. NTT has been quite a powerful mathematical tool in developing Post-Quantum Cryptography and Homomorphic Encryption. The Fourier Transform…
We introduce a two-layer wavelet scattering network, for object classification. This scattering transform computes a spatial wavelet transform on the first layer and a new joint wavelet transform along spatial, angular and scale variables…
Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance…
Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose…
Currently, most speech processing techniques use magnitude spectrograms as front-end and are therefore by default discarding part of the signal: the phase. In order to overcome this limitation, we propose an end-to-end learning method for…
We give a fairly comprehensive review of wavelets and of their application to density-functional theory (DFT) and to our recent application of a wavelet-based version of linear-response time-dependent DFT (LR-TD-DFT). Our intended audience…
Advanced neural machine translation (NMT) models generally implement encoder and decoder as multiple layers, which allows systems to model complex functions and capture complicated linguistic structures. However, only the top layers of…
The rapid advancement of image inpainting tools, especially those aimed at removing artifacts, has made digital image manipulation alarmingly accessible. This paper proposes several innovative ideas for detecting inpainting forgeries based…
In this paper, we study the synthesis of Gegenbauer processes using the wavelet packets transform. In order to simulate a 1-factor Gegenbauer process, we introduce an original algorithm, inspired by the one proposed by Coifman and…
Originating from a system theory and an input/output point of view, I introduce a new class of generalized distributions. A parametric nonlinear transformation converts a random variable $X$ into a so-called Lambert $W$ random variable $Y$,…
Channeling of high-energy particles in straight and bent multi-wall nanotubes (MWNT) has been studied in computer simulations and compared to the channeling properties of single-wall nanotubes (SWNT) and bent crystal lattices. It is…
Winograd's minimal filtering algorithm has been widely used in Convolutional Neural Networks (CNNs) to reduce the number of multiplications for faster processing. However, it is only effective on convolutions with kernel size as 3x3 and…
Image deblurring is a challenging problem in imaging due to its highly ill-posed nature. Deep learning models have shown great success in tackling this problem but the quest for the best image quality has brought their computational…
Past years have witnessed rapid developments in Neural Machine Translation (NMT). Most recently, with advanced modeling and training techniques, the RNN-based NMT (RNMT) has shown its potential strength, even compared with the well-known…
The ability to decompose a signal in an orthonormal basis (a set of orthogonal components, each normalized to have unit length) using a fast numerical procedure rests at the heart of many signal processing methods and applications. The…
We refine the recently introduced "Virtual VNA 3.0" technique to remove the need for coherent detection. The resulting "Virtual VNA 3.1" technique can unambiguously estimate the full scattering matrix of a non-reciprocal, linear, passive,…
A fully nonlinear potential Numerical Wave Tank (NWT) is developed in two dimensions, using a combination of the Harmonic Polynomial Cell (HPC) method for solving the Laplace problem on the wave potential and the Immersed Boundary Method…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…