Related papers: Spectral Convolution Networks
Recently, the generalization behavior of Convolutional Neural Networks (CNN) is gradually transparent through explanation techniques with the frequency components decomposition. However, the importance of the phase spectrum of the image for…
Bayesian inference, while foundational to probabilistic reasoning, is often hampered by the computational intractability of posterior distributions, particularly through the challenging evidence integral. Conventional approaches like Markov…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
Hyperspectral imaging is an important tool having been applied in various fields, but still limited in observation of dynamic scenes. In this paper, we propose a snapshot hyperspectral imaging technique which exploits both spectral and…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
Accurate spectrum prediction is crucial for dynamic spectrum access (DSA) and resource allocation. However, due to the unique characteristics of spectrum data, existing methods based on the time or frequency domain often struggle to…
Convolutional Neural Networks (CNNs) are a class of artificial neural networks whose computational blocks use convolution, together with other linear and non-linear operations, to perform classification or regression. This paper explores…
Deep networks are now able to achieve human-level performance on a broad spectrum of recognition tasks. Independently, neuromorphic computing has now demonstrated unprecedented energy-efficiency through a new chip architecture based on…
In view of recently demonstrated joint use of novel Fourier-transform techniques and effective high-accuracy frequency domain solvers related to the Method of Moments, it is argued that a set of transformative innovations could be developed…
We present a novel method to provide efficient and highly detailed reconstructions. Inspired by wavelets, we learn a neural field that decompose the signal both spatially and frequency-wise. We follow the recent grid-based paradigm for…
The enhancement of spectrum efficiency and the realization of secure spectrum utilization are critically dependent on spectrum cognition. However, existing spectrum cognition methods often exhibit limited generalization and suboptimal…
Recent studies show that self-attentions behave like low-pass filters (as opposed to convolutions) and enhancing their high-pass filtering capability improves model performance. Contrary to this idea, we investigate existing…
Activation functions play a vital role in the training of Convolutional Neural Networks. For this reason, to develop efficient and performing functions is a crucial problem in the deep learning community. Key to these approaches is to…
In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…
The "theoretical limit of time-frequency resolution in Fourier analysis" is thought to originate in certain mathematical and/or physical limitations. This, however, is not true. The actual origin arises from the numerical (technical) method…
This article demonstrates that convolutional operation can be converted to matrix multiplication, which has the same calculation way with fully connected layer. The article is helpful for the beginners of the neural network to understand…
A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, expansions in normalized associated Legendre functions of all…
Untrained neural networks (UNNs) offer high-fidelity electromagnetic inverse scattering reconstruction but are computationally limited by high-dimensional spatial-domain optimization. We propose a Real-Time Physics-Driven Fourier-Spectral…
In recent years, computer-aided diagnosis has become an increasingly popular topic. Methods based on convolutional neural networks have achieved good performance in medical image segmentation and classification. Due to the limitations of…