Related papers: Comparisons between fast algorithms for the contin…
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…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
Wavelet scattering networks, which are convolutional neural networks (CNNs) with fixed filters and weights, are promising tools for image analysis. Imposing symmetry on image statistics can improve human interpretability, aid in…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
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…
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
Edge devices are being deployed at increasing volumes to sense and act on information from the physical world. The discrete Fourier transform (DFT) is often necessary to make this sensed data suitable for further processing -- such as by…
In this work, we present the \emph{twiddless fast Fourier transform (TFFT)}, a novel algorithm for computing the $N$-point discrete Fourier transform (DFT). The TFFT's divide strategy builds on recent results that decimate an $N$-point…
Deep image registration has demonstrated exceptional accuracy and fast inference. Recent advances have adopted either multiple cascades or pyramid architectures to estimate dense deformation fields in a coarse-to-fine manner. However, due…
Fast Fourier Transform (FFT) is an essential tool in scientific and engineering computation. The increasing demand for mixed-precision FFT has made it possible to utilize half-precision floating-point (FP16) arithmetic for faster speed and…
The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…
Although certain vision transformer (ViT) and CNN architectures generalize well on vision tasks, it is often impractical to use them on green, edge, or desktop computing due to their computational requirements for training and even testing.…
Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…
Constructing a high-performance target detector under the background of sea clutter is always necessary and important. In this work, we propose a RepVGGA0-CWT detector, where RepVGG is a residual network that gains a high detection…
The embodied intelligence bridges the physical world and information space. As its typical physical embodiment, humanoid robots have shown great promise through robot learning algorithms in recent years. In this study, a hardware platform,…
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…
Fast time-domain algorithms have been developed in signal processing applications to reduce the multiplication complexity. For example, fast convolution structures using Cook-Toom and Winograd algorithms are well understood. Short length…
Power measurement algorithms based on Fourier transform are susceptible to errors caused by interharmonics, while wavelet transform algorithms are particularly sensitive to even harmonics due to band decomposition effects. The empirical…