相关论文: Super-Resolution in Phase Space

We present a pursuit-like algorithm that we call the "superset method" for recovery of sparse vectors from consecutive Fourier measurements in the super-resolution regime. The algorithm has a subspace identification step that hinges on the…

This paper presents a novel approach that combines the Deep Ritz Method (DRM) with Fourier feature mapping to solve minimization problems comprised of multi-well, non-convex energy potentials. These problems present computational challenges…

We propose a new fourth-order compact time-splitting ($S_\text{4c}$) Fourier pseudospectral method for the Dirac equation by splitting the Dirac equation into two parts together with using the double commutator between them to integrate the…

We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is…

We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…

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…

We are concerned with the dependence of the lowest positive eigenvalue of the Dirac operator on the geometry of rectangles, subject to infinite-mass boundary conditions. We conjecture that the square is a global minimiser both under the…

Despite being the most popular methods of data analysis, Fourier-based techniques suffer from the problem of static resolution that is currently believed to be a fundamental limitation of the Fourier Transform. Although alternative…

We are interested in the finite element solution of elliptic problems with a right-hand side of the single layer distribution type. Such problems arise when one aims at accounting for a physical hypersurface (or line, for bi-dimensional…

This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint.…

The problem of super-resolution, roughly speaking, is to reconstruct an unknown signal to high accuracy, given (potentially noisy) information about its low-degree Fourier coefficients. Prior results on super-resolution have imposed strong…

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…

Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely…

The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…

Diffractive zone plate optics uses a thin micro-structure pattern to alter the propagation direction of the incoming light wave. It has found important applications in extreme-wavelength imaging where conventional refractive lenses do not…

The problem of super-resolution in general terms is to recuperate a finitely supported measure $\mu$ given finitely many of its coefficients $\hat{\mu}(k)$ with respect to some orthonormal system. The interesting case concerns situations,…

This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is an off-the-grid generalisation of l1 regularization (also…

In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…

We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional…

This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a…