Related papers: The near shift-invariance of the dual-tree complex…
The dual-tree complex wavelet transform (DT-CWT) is known to exhibit better shift-invariance than the conventional discrete wavelet transform. We propose an amplitude-phase representation of the DT-CWT which, among other things, offers a…
This paper presents a method for background removal in experimental data processing using the Dual-Tree Complex Wavelet Transform (DTCWT). The technique is based on discrete wavelet theory (DWT) and addresses limitations of commonly used…
The dual-tree complex wavelet transform (DT-$\mathbb{C}$WT) is extended to the 4D setting. Key properties of 4D DT-$\mathbb{C}$WT, such as directional sensitivity and shift-invariance, are discussed and illustrated in a tomographic…
We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-CWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the…
The wavelet transform has seen success when incorporated into neural network architectures, such as in wavelet scattering networks. More recently, it has been shown that the dual-tree complex wavelet transform can provide better…
This paper introduces a Deep Scattering network that utilizes Dual-Tree complex wavelets to extract translation invariant representations from an input signal. The computationally efficient Dual-Tree wavelets decompose the input signal into…
This work introduces Differential Wavelet Amplifier (DWA), a drop-in module for wavelet-based image Super-Resolution (SR). DWA invigorates an approach recently receiving less attention, namely Discrete Wavelet Transformation (DWT). DWT…
Tensor product real-valued wavelets have been employed in many applications such as image processing with impressive performance. Though edge singularities are ubiquitous and play a fundamental role in two-dimensional problems, tensor…
The nondecimated or translation-invariant wavelet transform (NDWT) is a central tool in classical multiscale signal analysis, valued for its stability, redundancy, and shift invariance. This paper develops two complementary quantum…
In deep time series forecasting, the Fourier Transform (FT) is extensively employed for frequency representation learning. However, it often struggles in capturing multi-scale, time-sensitive patterns. Although the Wavelet Transform (WT)…
An algorithm is presented to update the multi-fractal spectrum of a time series in constant time when new data arrives. The discrete wavelet transform (DWT) of the time series is first updated for the new data value. This is done optimally…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
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…
The main objective of this paper is to define the mother wavelet on local fields and study the continuous wavelet transform (CWT) and some of their basic properties. its inversion formula, the Parseval relation and associated convolution…
The continuous wavelet transform (CWT) is very useful for processing signals with intricate and irregular structures in astrophysics and cosmology. It is crucial to propose precise and fast algorithms for the CWT. In this work, we review…
Upcoming LCLS-II/II-HE operation at repetition rates approaching 1MHz demands on-detector data reduction to manage the resulting data volumes. We present a 2D discrete wavelet transform (DWT) pre-processing algorithm that segments…
The symplectic wavelet transformation [Opt. Lett. 31 (2006) 3432], which is related to quantum optical Fresnel transform, is developed to the symplectic-dilation mixed wavelet transform (SDWT). The SDWT involves both a real-variable…
We present the Maximal Overlap Discrete Wavelet Scattering Transform (MODWST), whose construction is inspired by the combination of the Maximal Overlap Discrete Wavelet Transform (MODWT) and the Scattering Wavelet Transform (WST). We also…
In this paper, we exploit the theory of convolution of index Whittaker transform for study of continuous and discrete Index Whittaker wavelet transform and discuss some of its basic properties. Certain boundedness, Plancherel as well as…
The polar wavelet transform (PWT) has been proven to be a powerful mathematical tool for signal and image processing in recent years. Due to the increasing demand for directional representations of signals in engineering, it is impossible…