Search Results for author: Habib Ammari

Found 10 papers, 0 papers with code

An Operator Theory for Analyzing the Resolution of Multi-illumination Imaging Modalities

no code implementations2 Feb 2023 Ping Liu, Habib Ammari

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

no code implementations1 Dec 2022 Ping Liu, Habib Ammari

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

no code implementations28 Nov 2022 Ping Liu, Habib Ammari

The second crucial contribution of this paper is the theoretical proof of a two-point resolution limit in multi-dimensional spaces.

Common Sense Reasoning Super-Resolution

A mathematical theory of resolution limits for super-resolution of positive sources

no code implementations24 Nov 2022 Ping Liu, Yanchen He, Habib Ammari

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

no code implementations14 May 2022 Ping Liu, Habib Ammari

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.

Direction of Arrival Estimation Super-Resolution

Dynamic super-resolution in particle tracking problems

no code implementations8 Apr 2022 Ping Liu, Habib Ammari

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.

Dynamic Reconstruction Super-Resolution

Mathematical Foundation of Sparsity-based Multi-snapshot Spectral Estimation

no code implementations22 Feb 2022 Ping Liu, Sanghyeon Yu, Ola Sabet, Lucas Pelkmans, Habib Ammari

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.

Compressive Sensing Super-Resolution

Robust Cardiac Motion Estimation using Ultrafast Ultrasound Data: A Low-Rank-Topology-Preserving Approach

no code implementations26 Oct 2016 Angelica I. Aviles, Thomas Widlak, Alicia Casals, Maartje M. Nillesen, Habib Ammari

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.

Motion Estimation

Time-domain multiscale shape identification in electro-sensing

no code implementations12 Sep 2014 Habib Ammari, Han Wang

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

no code implementations10 Oct 2013 Habib Ammari, Stéphane Mallat, Irène Waldspurger, Han Wang

This paper aims at presenting a new approach to the electro-sensing problem using wavelets.

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