Related papers: Hybrid Dealiasing of Complex Convolutions
Brain-inspired hyperdimensional (HD) computing models neural activity patterns of the very size of the brain's circuits with points of a hyperdimensional space, that is, with hypervectors. Hypervectors are $D$-dimensional (pseudo)random…
Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
In image deconvolution problems, the diagonalization of the underlying operators by means of the FFT usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard…
Currently, transformer-based algorithms are making a splash in the domain of image deblurring. Their achievement depends on the self-attention mechanism with CNN stem to model long range dependencies between tokens. Unfortunately, this…
The high-dimensional data setting, in which p >> n, is a challenging statistical paradigm that appears in many real-world problems. In this setting, learning a compact, low-dimensional representation of the data can substantially help…
We study computing the convolution of a private input $x$ with a public input $h$, while satisfying the guarantees of $(\epsilon, \delta)$-differential privacy. Convolution is a fundamental operation, intimately related to Fourier…
We present a model for non-blind image deconvolution that incorporates the classic iterative method into a deep learning application. Instead of using large over-parameterised generative networks to create sharp picture representations, we…
2D convolution is a staple of digital image processing. The advent of large format imagers makes it possible to literally ``pave'' with silicon the focal plane of an optical sensor, which results in very large images that can require a…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
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…
Deep image hashing aims to map input images into simple binary hash codes via deep neural networks and thus enable effective large-scale image retrieval. Recently, hybrid networks that combine convolution and Transformer have achieved…
In recent years, algorithm unrolling has emerged as a powerful technique for designing interpretable neural networks based on iterative algorithms. Imaging inverse problems have particularly benefited from unrolling-based deep network…
This paper introduces a novel approach to approximating continuous functions over high-dimensional hypercubes by integrating matrix CUR decomposition with hyperinterpolation techniques. Traditional Fourier-based hyperinterpolation methods…
Hashing-based methods seek compact and efficient binary codes that preserve the neighborhood structure in the original data space. For most existing hashing methods, an image is first encoded as a vector of hand-crafted visual feature,…
Hyperdimensional computing (HD) is an emerging paradigm for machine learning based on the evidence that the brain computes on high-dimensional, distributed, representations of data. The main operation of HD is encoding, which transfers the…
Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…
The paper introduces the weighted convolution, a novel approach to the convolution for signals defined on regular grids (e.g., 2D images) through the application of an optimal density function to scale the contribution of neighbouring…
Deep convolutional networks are vulnerable to image translation or shift, partly due to common down-sampling layers, e.g., max-pooling and strided convolution. These operations violate the Nyquist sampling rate and cause aliasing. The…