Phaseless super-resolution in the continuous domain

Phaseless super-resolution refers to the problem of superresolving a signal from only its low-frequency Fourier magnitude measurements. In this paper, we consider the phaseless super-resolution problem of recovering a sum of sparse Dirac delta functions which can be located anywhere in the continuous time-domain. For such signals in the continuous domain, we propose a novel Semidefinite Programming (SDP) based signal recovery method to achieve the phaseless superresolution. This work extends the recent work of Jaganathan et al. [1], which considered phaseless super-resolution for discrete signals on the grid

2D phaseless super-resolution

In phaseless super-resolution, we only have the magnitude information of continuously-parameterized signals in a transform domain, and try to recover the original signals from these magnitude measurements. Optical microscopy is one application where the phaseless super-resolution for 2D signals arise. In this paper, we propose algorithms for performing phaseless super-resolution for 2D or higher-dimensional signals, and investigate their performance guarantees

2D phaseless super-resolution

In phaseless super-resolution, we only have the magnitude information of continuously-parameterized signals in a transform domain, and try to recover the original signals from these magnitude measurements. Optical microscopy is one application where the phaseless super-resolution for 2D signals arise. In this paper, we propose algorithms for performing phaseless super-resolution for 2D or higher-dimensional signals, and investigate their performance guarantees

On the Sampling of the Fresnel Field Intensity over a Full Angular Sector

In this article, the question of how to sample the square amplitude of the radiated field in the framework of phaseless antenna diagnostics is addressed. In particular, the goal of the article is to find a discretization scheme that exploits a non-redundant number of samples and returns a discrete model whose mathematical properties are similar to those of the continuous one. To this end, at first, the lifting technique is used to obtain a linear representation of the square amplitude of the radiated field. Later, a discretization scheme based on the Shannon sampling theorem is exploited to discretize the continuous model. More in detail, the kernel of the related eigenvalue problem is first recast as the Fourier transform of a window function, and after, it is evaluated. Finally, the sampling theory approach is applied to obtain a discrete model whose singular values approximate all the relevant singular values of the continuous linear model. The study refers to a strip source whose square magnitude of the radiated field is observed in the Fresnel zone over a 2D observation domain

Off-The-Grid Spectral Compressed Sensing With Prior Information

Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In this paper, we extend off-the-grid CS to applications where some prior information about spectrally sparse signal is known. We specifically consider cases where a few contributing frequencies or poles, but not their amplitudes or phases, are known a priori. Our results show that equipping off-the-grid CS with the known-poles algorithm can increase the probability of recovering all the frequency components.Comment: 5 pages, 4 figure