Related papers: An Adaptive Sublinear-Time Block Sparse Fourier Tr…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
In this paper, a novel and robust algorithm is proposed for adaptive beamforming based on the idea of reconstructing the autocorrelation sequence (ACS) of a random process from a set of measured data. This is obtained from the first column…
We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…
We want to exactly reconstruct a sparse signal f (a vector in R^n of small support) from few linear measurements of f (inner products with some fixed vectors). A nice and intuitive reconstruction by Linear Programming has been advocated…
This paper considers the problem of recovering a $k$-sparse, $N$-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very…
A new iterative low complexity algorithm has been presented for computing the Walsh-Hadamard transform (WHT) of an $N$ dimensional signal with a $K$-sparse WHT, where $N$ is a power of two and $K = O(N^\alpha)$, scales sub-linearly in $N$…
In the average-case $k$-SUM problem, given $r$ integers chosen uniformly at random from $\{0,\dots,M-1\}$, the objective is to find a ``solution'' set of $k$ numbers that sum to $0$ modulo $M$. In the dense regime of $M \leq r^k$, where…
We consider sparse variants of the classical Learning Parities with random Noise (LPN) problem. Our main contribution is a new algorithmic framework that provides learning algorithms against low-noise for both Learning Sparse Parities…
The paper observes the Hermite and the Fourier Transform domains in terms of Frequency Hopping Spread Spectrum signals sparsification. Sparse signals can be recovered from a reduced set of samples by using the Compressive Sensing approach.…
We consider the problem of robustly recovering a $k$-sparse coefficient vector from the Fourier series that it generates, restricted to the interval $[- \Omega, \Omega]$. The difficulty of this problem is linked to the superresolution…
The $N$-point discrete Fourier transform (DFT) is a cornerstone for several signal processing applications. Many of these applications operate in real-time, making the computational complexity of the DFT a critical performance indicator to…
In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…
We present the novel adaptive hierarchical sensing algorithm K-AHS, which samples sparse or compressible signals with a measurement complexity equal to that of Compressed Sensing (CS). In contrast to CS, K-AHS is adaptive as sensing vectors…
A central problem in parameterized algorithms is to obtain algorithms with running time $f(k)\cdot n^{O(1)}$ such that $f$ is as slow growing function of the parameter $k$ as possible. In particular, a large number of basic parameterized…
We give new sublinear and parallel algorithms for the extensively studied problem of approximating n-variable r-CSPs (constraint satisfaction problems with constraints of arity r up to an additive error. The running time of our algorithms…
Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance…
An accelerated class of adaptive scheme of iterative thresholding algorithms is studied analytically and empirically. They are based on the feedback mechanism of the null space tuning techniques (NST+HT+FB). The main contribution of this…
We study convergence properties of sparse averages of partial sums of Fourier series of continuous functions. By sparse averages, we are considering an increasing sequences of integers $n_0 < n_1 < n_2 < ...$ and looking at…
We consider the problem of exactly learning an $s$-sparse real-valued Boolean polynomial of degree $d$ of the form $f:\{ 0,1\}^n \rightarrow \mathbb{R}$. This problem corresponds to decomposing functions in the AND basis and is known as…
Efficiently modeling spatio-temporal (ST) physical processes and observations presents a challenging problem for the deep learning community. Many recent studies have concentrated on meticulously reconciling various advantages, leading to…