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Found 10 papers, 0 papers with code
An Operator Theory for Analyzing the Resolution of Multi-illumination Imaging Modalities
We show that the resolution of multi-illumination imaging is approximately determined by the new imaging kernel from our operator theory and better resolution can be realized by sparsity-promoting techniques in practice but only for resolving very sparse sources.
Super-resolution of positive near-colliding point sources
In this paper, we analyze the capacity of super-resolution of one-dimensional positive sources.
A mathematical theory of super-resolution and two-point resolution
The second crucial contribution of this paper is the theoretical proof of a two-point resolution limit in multi-dimensional spaces.
A mathematical theory of resolution limits for super-resolution of positive sources
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.
Nearly optimal resolution estimate for the two-dimensional super-resolution and a new algorithm for direction of arrival estimation with uniform rectangular array
The stability result exhibits the optimal performance of sparsity promoting in solving such problems; (iii) Our techniques pave the way for improving the estimate for resolution limits in higher-dimensional super-resolutions to nearly optimal; (iv) Inspired by these new techniques, we propose a new coordinate-combination-based model order detection algorithm for two-dimensional DOA estimation and theoretically demonstrate its optimal performance, and (v) we also propose a new coordinate-combination-based MUSIC algorithm for super-resolving sources in two-dimensional DOA estimation.
Dynamic super-resolution in particle tracking problems
This result is derived by an observation that the inherent cut-off frequency for the velocity recovery can be viewed as the total observation time multiplies the cut-off frequency of the imaging system, which may lead to a better resolution limit as compared to the one for each diffraction-limited frame.
Mathematical Foundation of Sparsity-based Multi-snapshot Spectral Estimation
In this paper, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements in a bounded domain.
Robust Cardiac Motion Estimation using Ultrafast Ultrasound Data: A Low-Rank-Topology-Preserving Approach
While this is an important part of our solution, the main highlight of this paper is to combine a low-rank data representation with topology preservation.
Time-domain multiscale shape identification in electro-sensing
This paper presents premier and innovative time-domain multi-scale method for shape identification in electro-sensing using pulse-type signals.
Wavelet methods for shape perception in electro-sensing
This paper aims at presenting a new approach to the electro-sensing problem using wavelets.
