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A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…
The non-equidistant fast Fourier transform (NFFT) is an extension of the famous fast Fourier transform (FFT), which can be applied to non-equidistantly sampled data in time/space or frequency domain. It is an approximative algorithm that…
Dense prediction tasks typically employ encoder-decoder architectures, but the prevalent convolutions in the decoder are not image-adaptive and can lead to boundary artifacts. Different generalized convolution operations have been…
For a sample set of 1024 values, the FFT is 102.4 times faster than the discrete Fourier transform (DFT). The basis for this remarkable speed advantage is the `bit-reversal' scheme of the Cooley-Tukey algorithm. Eliminating the burden of…
For smooth finite fields $F_q$ (i.e., when $q-1$ factors into small primes) the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division,…
Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to…
This paper presents a novel frequency-domain approach for path following problem, specifically designed to handle paths described by discrete data. The proposed algorithm utilizes the fast Fourier Transform (FFT) to process the discrete…
We study the problem of constructing a graph Fourier transform (GFT) for directed graphs (digraphs), which decomposes graph signals into different modes of variation with respect to the underlying network. Accordingly, to capture low,…
Using the existence of infinite numbers $k$ in the non-Archimedean ring of Robinson-Colombeau, we define the hyperfinite Fourier transform (HFT) by considering integration extended to $[-k,k]^{n}$ instead of $(-\infty,\infty)^{n}$. In order…
While most time series are non-stationary, it is inevitable for models to face the distribution shift issue in time series forecasting. Existing solutions manipulate statistical measures (usually mean and std.) to adjust time series…
We study the recovery of the distribution function $F_X$ of a random variable $X$ that is subject to an independent additive random error $\varepsilon$. To be precise, it is assumed that the target variable $X$ is available only in the form…
Contemporary diffusion models built upon U-Net or Diffusion Transformer (DiT) architectures have revolutionized image generation through transformer-based attention mechanisms. The prevailing paradigm has commonly employed self-attention…
This paper proposes a novel approach to address the challenge that pretrained VLA models often fail to effectively improve performance and reduce adaptation costs during standard supervised finetuning (SFT). Some advanced finetuning methods…
Diffusion-based inverse algorithms have shown remarkable performance across various inverse problems, yet their reliance on numerous denoising steps incurs high computational costs. While recent developments of fast diffusion ODE solvers…
Since the evolution of digital computers, the storage of data has always been in terms of discrete bits that can store values of either 1 or 0. Hence, all computer programs (such as MATLAB), convert any input continuous signal into a…
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
The notion of fractional Fourier transform (FrFT) has been used and investigated for many years by various research communities, which finds widespread applications in many diverse fields of research study. The potential applications…
In radar systems, high resolution in the Doppler dimension is important for detecting slow-moving targets as it allows for more distinct separation between these targets and clutter, or stationary objects. However, achieving sufficient…
The Random Variable Transformation (RVT) method is a fundamental tool for determining the probability distribution function associated with a Random Variable (RV) Y=g(X), where X is a RV and g is a suitable transformation. In the usual…
Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…