Related papers: A High-dimensional Sparse Fourier Transform in the…
We consider the problem of computing the Walsh-Hadamard Transform (WHT) of some $N$-length input vector in the presence of noise, where the $N$-point Walsh spectrum is $K$-sparse with $K = {O}(N^{\delta})$ scaling sub-linearly in the input…
We report the realization of a new iterative Fourier-transform algorithm for creating holograms that can diffract light into an arbitrary two-dimensional intensity profile. We show that the predicted intensity distributions are smooth with…
We consider the classical problem of finding the sparse representation of a signal in a pair of bases. When both bases are orthogonal, it is known that the sparse representation is unique when the sparsity $K$ of the signal satisfies…
This note considers the multidimensional unstructured sparse recovery problems. Examples include Fourier inversion and sparse deconvolution. The eigenmatrix is a data-driven construction with desired approximate eigenvalues and eigenvectors…
Learning-based image super-resolution aims to reconstruct high-frequency (HF) details from the prior model trained by a set of high- and low-resolution image patches. In this paper, HF to be estimated is considered as a combination of two…
Quadratic regression involves modeling the response as a (generalized) linear function of not only the features $x^{j_1}$ but also of quadratic terms $x^{j_1}x^{j_2}$. The inclusion of such higher-order "interaction terms" in regression…
Generalizable neural surface reconstruction has become a compelling technique to reconstruct from few images without per-scene optimization, where dense 3D feature volume has proven effective as a global representation of scenes. However,…
The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results.…
Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…
Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…
We present a comprehensive analysis of an algorithm for evaluating high-dimensional polynomials that are invariant under permutations and rotations. The key bottleneck is the contraction of a high-dimensional symmetric and sparse tensor…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
Efficient indexing and searching of high dimensional data has been an area of active research due to the growing exploitation of high dimensional data and the vulnerability of traditional search methods to the curse of dimensionality. This…
The Fast Fourier Transform(FFT) is a classic signal processing algorithm that is utilized in a wide range of applications. For image processing, FFT computes on every pixel's value of an image, regardless of their properties in frequency…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…
Sampling theory in fractional Fourier Transform (FrFT) domain has been studied extensively in the last decades. This interest stems from the ability of the FrFT to generalize the traditional Fourier Transform, broadening the traditional…
We consider the sparse moment problem of learning a $k$-spike mixture in high-dimensional space from its noisy moment information in any dimension. We measure the accuracy of the learned mixtures using transportation distance. Previous…
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…
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…