相关论文: Sparse Approximation to the Dirac-{\delta} Distrib…
Face recognition is the very significant field in pattern recognition area. It has multiple applications in military and finance, to name a few. In this paper, the combination of the sparse PCA with the nearest-neighbor method (and with the…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
Representing a sparse histogram, or more generally a sparse vector, is a fundamental task in differential privacy. An ideal solution would use space close to information-theoretical lower bounds, have an error distribution that depends…
High-dimensional Partial Differential Equations (PDEs) are a popular mathematical modelling tool, with applications ranging from finance to computational chemistry. However, standard numerical techniques for solving these PDEs are typically…
This work considers the problem of super-resolution. The goal is to resolve a Dirac distribution from knowledge of its discrete, low-pass, Fourier measurements. Classically, such problems have been dealt with parameter estimation methods.…
We propose a novel adaptive empirical Bayesian method for sparse deep learning, where the sparsity is ensured via a class of self-adaptive spike-and-slab priors. The proposed method works by alternatively sampling from an adaptive…
Affine frequency division multiplexing (AFDM) and orthogonal AFDM access (O-AFDMA) are promising techniques based on chirp signals, which are able to suppress the performance deterioration caused by Doppler shifts in high-mobility…
This paper addresses the problem of expressing a signal as a sum of frequency components (sinusoids) wherein each sinusoid may exhibit abrupt changes in its amplitude and/or phase. The Fourier transform of a narrow-band signal, with a…
In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\hat{f}} \in \mathbb{C}^N$ of any given input vector…
In this paper, we propose a solution for a fundamental problem in computational harmonic analysis, namely, the construction of a multiresolution analysis with directional components. We will do so by constructing subdivision schemes which…
In the present work, we propose a novel method for reconstruction of multi-dimensional kinetic distributions, based on their representation as a mixture of Dirac delta functions. The representation is found as a solution of an optimization…
In this paper we approximate high-dimensional functions $f\colon\mathbb T^d\to\mathbb C$ by sparse trigonometric polynomials based on function evaluations. Recently it was shown that a dimension-incremental sparse Fourier transform (SFT)…
The FFT algorithm that implements the discrete Fourier transform is considered one of the top ten algorithms of the $20$th century. Its main strengths are the low computational cost of $\mathcal{O}(n \log n$) and its stability. It is one of…
We discuss a method for sparse signal approximation, which is based on the correlation of the target signal with a pseudo-random signal, and uses a modification of the greedy matching pursuit algorithm. We show that this approach provides…
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…
In this paper, we introduce DICOD, a convolutional sparse coding algorithm which builds shift invariant representations for long signals. This algorithm is designed to run in a distributed setting, with local message passing, making it…
Approximations of the Dirac delta distribution are commonly used to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In this work, we show a priori rates of convergence of this…
We propose a multi-dimensional (M-D) sparse Fourier transform inspired by the idea of the Fourier projection-slice theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional slices from an M-D data cube), which are…
Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging.…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…