Related papers: Deterministic Sparse Sublinear FFT with Improved N…

Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems. However, diffusion-based reconstruction…

This paper demonstrates the usefulness of distributed local verification of proofs, as a tool for the design of self-stabilizing algorithms.In particular, it introduces a somewhat generalized notion of distributed local proofs, and utilizes…

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 linear regression is the well-studied inference problem where one is given a design matrix $\mathbf{A} \in \mathbb{R}^{M\times N}$ and a response vector $\mathbf{b} \in \mathbb{R}^M$, and the goal is to find a solution $\mathbf{x}…

Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a…

We show that the condition number of any cyclically contiguous $p\times q$ submatrix of the $N\times N$ discrete Fourier transform (DFT) matrix is at least $$ \exp \left( \frac{\pi}{2} \left[\min(p,q)- \frac{pq}{N}\right] \right)~, $$ up to…

The Transformer has been an indispensable staple in deep learning. However, for real-life applications, it is very challenging to deploy efficient Transformers due to immense parameters and operations of models. To relieve this burden,…

Numerical analysis for linear constant-coefficients Finite Difference schemes was developed approximately fifty years ago. It relies on the assumption of scheme stability and in particular -- for the $L^2$ setting -- on the absence of…

We detail a novel Fourier-based approach (IterativeFT) for identifying deterministic network structure in the presence of both edge pruning and Gaussian noise. This technique involves the iterative execution of forward and inverse 2D…

Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…

This paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [B. Harding and M. Hegland, ANZIAM J., 54 (CTAC2012), pp. C394-C411]. The approach is novel for two reasons, first it…

The Kaczmarz algorithm is an iterative method to reconstruct an unknown vector $f$ from inner products $\langle f , \varphi_{n} \rangle $. We consider the problem of how additive noise affects the reconstruction under the assumption that…

In this paper, we propose new deterministic and Monte Carlo interpolation algorithms for sparse multivariate polynomials represented by straight-line programs. Let $f$ be an $n$-variate polynomial given by a straight-line program, which has…

A major challenge in many modern superresolution fluorescence microscopy techniques at the nanoscale lies in the correct alignment of long sequences of sparse but spatially and temporally highly resolved images. This is caused by the…

This paper considers the problem of recovering a one or two dimensional discrete signal which is approximately sparse in its discrete gradient from an incomplete subset of its discrete Fourier coefficients which have been corrupted with…

An approximate sparse recovery system consists of parameters $k,N$, an $m$-by-$N$ measurement matrix, $\Phi$, and a decoding algorithm, $\mathcal{D}$. Given a vector, $x$, the system approximates $x$ by $\widehat x =\mathcal{D}(\Phi x)$,…

The Kaczmarz algorithm is a popular solver for overdetermined linear systems due to its simplicity and speed. In this paper, we propose a modification that speeds up the convergence of the randomized Kaczmarz algorithm for systems of linear…

The paper considers the problem of identifying the sparse different components between two high dimensional means of column-wise dependent random vectors. We show that the dependence can be utilized to lower the identification boundary for…

A $t$-spanner of an undirected $n$-vertex graph $G$ is a sparse subgraph $H$ of $G$ that preserves all pairwise distances between its vertices to within multiplicative factor $t$, also called the \emph{stretch}. We investigate the problem…

In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, where the numerator can be written as the sum of a continuously differentiable convex function whose gradient is Lipschitz continuous and a proper…