Related papers: Sample Efficient Estimation and Recovery in Sparse…
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 $\widehat x =\mathcal{D}(\Phi x)$,…
We consider the problem of estimating the frequency components of a mixture of s complex sinusoids from a random subset of n regularly spaced samples. Unlike previous work in compressed sensing, the frequencies are not assumed to lie on a…
We develop a sparse spectral method for a class of fractional differential equations, posed on $\mathbb{R}$, in one dimension. These equations can include sqrt-Laplacian, Hilbert, derivative and identity terms. The numerical method utilizes…
This paper introduces a hybrid computational framework for the multi-frequency inverse source problem governed by the Helmholtz equation. By integrating a classical Fourier method with a deep convolutional neural network, we address the…
This paper considers the use of total variation regularization in the recovery of approximately gradient sparse signals from their noisy discrete Fourier samples in the context of compressed sensing. It has been observed over the last…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
The special affine Fourier transform (SAFT) is a promising tool for analyzing non-stationary signals with more degrees of freedom. However, the SAFT fails in obtaining the local features of non-transient signals due to its global kernel and…
Time-frequency (TF) representation of non-stationary signals typically requires the effective concentration of energy distribution along the instantaneous frequency (IF) ridge, which exhibits intrinsic sparsity. Inspired by the sparse…
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…
Many signal and image processing applications have benefited remarkably from the fact that the underlying signals reside in a low dimensional subspace. One of the main models for such a low dimensionality is the sparsity one. Within this…
A function $f : \mathbb{F}_2^n \to \mathbb{R}$ is $s$-sparse if it has at most $s$ non-zero Fourier coefficients. Motivated by applications to fast sparse Fourier transforms over $\mathbb{F}_2^n$, we study efficient algorithms for the…
Sampling from the output distribution of chaotic quantum evolutions, and of pseudo-random universal quantum circuits in particular, has been proposed as a prominent milestone for near-term quantum supremacy. The same paper notes that…
Nonstationary signals are commonly analyzed and processed in the time-frequency (T-F) domain that is obtained by the discrete Gabor transform (DGT). The T-F representation obtained by DGT is spread due to windowing, which may degrade the…
We propose a novel sparse representation for heavily underdetermined multichannel sound mixtures, i.e., with much more sources than microphones. The proposed approach operates in the complex Fourier domain, thus preserving spatial…
The short-time Fourier transform (STFT) is widely used for analyzing non-stationary signals. However, its performance is highly sensitive to its parameters, and manual or heuristic tuning often yields suboptimal results. To overcome this…
The power spectrum, as a statistic in Fourier space, is commonly numerically calculated using the fast Fourier transform method to efficiently reduce the computational costs. To alleviate the systematic bias known as aliasing due to the…
The nonlinear Schr\"odinger equation (NSE) is well-known to model an ideal fiber-optic communication channel. Even though the NSE is a nonlinear evolution equation, it can be solved analytically using a nonlinear Fourier transform (NFT).…
In this paper, we present two variations of an algorithm for signal reconstruction from one-bit or two-bit noisy observations of the discrete Fourier transform (DFT). The one-bit observations of the DFT correspond to the sign of its real…
A compressive sensing (CS) reconstruction method for polynomial phase signals is proposed in this paper. It relies on the Polynomial Fourier transform, which is used to establish a relationship between the observation and sparsity domain.…
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…