Related papers: Systematic DFT Frames: Principle, Eigenvalues Stru…
The short-time Fourier transform (STFT) is widely used for analyzing non-stationary signals. However, its performance is highly sensitive to its parameters, and manual or heuristic tuning often yields suboptimal results. To overcome this…
Recent work has empirically shown that deep neural networks latch on to the Fourier statistics of training data and show increased sensitivity to Fourier-basis directions in the input. Understanding and modifying this Fourier-sensitivity of…
Frames are the foundation of the linear operators used in the decomposition and reconstruction of signals, such as the discrete Fourier transform, Gabor, wavelets, and curvelet transforms. The emergence of sparse representation models has…
In image and video coding applications, distortion has been traditionally measured using mean square error (MSE), which suggests the use of orthogonal transforms, such as the discrete cosine transform (DCT). Perceptual metrics such as…
Progress towards the energy breakthroughs needed to combat climate change can be significantly accelerated through the efficient simulation of atomic systems. Simulation techniques based on first principles, such as Density Functional…
Holographic MIMO (hMIMO) systems with a massive number of individually controlled antennas N make minimum mean square error (MMSE) channel estimation particularly challenging, due to its computational complexity that scales as $N^3$ . This…
There exist many ways to build an orthonormal basis of $\mathbb{R}^N$, consisting of the eigenvectors of the discrete Fourier transform (DFT). In this paper we show that there is only one such orthonormal eigenbasis of the DFT that is…
We present a novel algorithm, named the 2D-FFAST, to compute a sparse 2D-Discrete Fourier Transform (2D-DFT) featuring both low sample complexity and low computational complexity. The proposed algorithm is based on mixed concepts from…
Over-complete systems of vectors, or in short, frames, play the role of analog codes in many areas of communication and signal processing. To name a few, spreading sequences for code-division multiple access (CDMA), over-complete…
This paper presents a novel approach that combines the Deep Ritz Method (DRM) with Fourier feature mapping to solve minimization problems comprised of multi-well, non-convex energy potentials. These problems present computational challenges…
Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from…
In the analysis of High-Energy Physics data, it is frequently desired to separate resonant signals from a smooth, non-resonant background. This paper introduces a new technique - functional decomposition (FD) - to accomplish this task. It…
Parameter-efficient fine-tuning (PEFT) has attracted significant attention due to the growth of pre-trained model sizes and the need to fine-tune (FT) them for superior downstream performance. Despite a surge in new PEFT methods, a…
Simultaneous Localization and Mapping (SLAM) is an essential technology for the efficiency and reliability of unmanned robotic exploration missions. While the onboard computational capability and communication bandwidth are critically…
Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…
Density functional theory (DFT) is an essential building block for modern theoretical physics, chemistry, and engineering, especially those concerning electronic properties. Through decades of development, various program packages for…
The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…
Recently, style transfer is a research area that attracts a lot of attention, which transfers the style of an image onto a content target. Extensive research on style transfer has aimed at speeding up processing or generating high-quality…
While random Fourier features are a classic tool in kernel methods, their utility as a pre-processing step for deep learning on tabular data has been largely overlooked. Motivated by shortcomings in tabular deep learning pipelines -…
Despite recent advancements, deep neural networks are not robust against adversarial perturbations. Many of the proposed adversarial defense approaches use computationally expensive training mechanisms that do not scale to complex…