Related papers: Stable Separation and Super-Resolution of Mixture …
Neural recordings, returns from radars and sonars, images in astronomy and single-molecule microscopy can be modeled as a linear superposition of a small number of scaled and delayed copies of a band-limited or diffraction-limited point…
The aim of two-dimensional line spectral estimation is to super-resolve the spectral point sources of the signal from time samples. In many associated applications such as radar and sonar, due to cut-off and saturation regions in electronic…
The problem of recovering a mixture of spike signals convolved with distinct point spread functions (PSFs) lying on a parametric manifold, under the assumption that the spike locations are known, is studied. The PSF unmixing problem is…
We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been shown that exact recovery is possible by…
We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an…
Two-point super-resolution is an important problem in many signal processing applications. In this paper, we aim to establish a resolution theory for two-point super-resolution from a single snapshot. We consider a complex two-point model…
We study the inverse problem of estimating n locations $t_1, ..., t_n$ (up to global scale, translation and negation) in $R^d$ from noisy measurements of a subset of the (unsigned) pairwise lines that connect them, that is, from noisy…
Particle tracking in biological imaging is concerned with reconstructing the trajectories, locations, or velocities of the targeting particles. The standard approach of particle tracking consists of two steps: first reconstructing…
We study an efficient dynamic blind source separation algorithm of convolutive sound mixtures based on updating statistical information in the frequency domain, andminimizing the support of time domain demixing filters by a weighted least…
The performance of audio source separation from underdetermined convolutive mixture assuming known mixing filters can be significantly improved by using an analysis sparse prior optimized by a reweighting l1 scheme and a wideband…
Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…
Atomic norm methods have recently been proposed for spectral super-resolution with flexibility in dealing with missing data and miscellaneous noises. A notorious drawback of these convex optimization methods however is their lower…
A priori information on the positivity of source intensities is ubiquitous in imaging fields and is also important for a multitude of super-resolution and deconvolution algorithms. However, the fundamental resolution limit of positive…
We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point.…
We consider the inverse problem of recovering the locations and amplitudes of a collection of point sources represented as a discrete measure, given $M+1$ of its noisy low-frequency Fourier coefficients. Super-resolution refers to a stable…
We consider the problem of super-resolving the line spectrum of a multisinusoidal signal from a finite number of samples, some of which may be completely corrupted. Measurements of this form can be modeled as an additive mixture of a…
$3$D structure recovery from a collection of $2$D images requires the estimation of the camera locations and orientations, i.e. the camera motion. For large, irregular collections of images, existing methods for the location estimation…
In this paper, we analyze the capacity of super-resolution of one-dimensional positive sources. In particular, we consider the same setting as in [arXiv:1904.09186v2 [math.NA]] and generalize the results there to the case of super-resolving…
We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the…
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…