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Super-resolution power and robustness of compressive sensing for spectral estimation with application to spaceborne tomographic SAR

Zhu, Xiao Xiang und Bamler, Richard (2012) Super-resolution power and robustness of compressive sensing for spectral estimation with application to spaceborne tomographic SAR. IEEE Transactions on Geoscience and Remote Sensing, 50 (1), Seiten 1-12. IEEE. DOI: 10.1109/TGRS.2011.2160183 . ISSN 0196-2892 .

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Offizielle URL: http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5966335

Kurzfassung

We address the problem of resolving two closely spaced complex-valued points from N irregular Fourier do- main samples. Although this is a generic super-resolution (SR) problem, our target application is SAR tomography (TomoSAR), where typically the number of acquisitions is N = 10 - 100 and SNR = 0-10 dB. As the TomoSAR algorithm, we introduce "Scale-down by LI norm Minimization, Model selection, and Estimation Reconstruction" (SL1MMER), which is a spectral estimation algorithm based on compressive sensing, model order selection, and final maximum likelihood parameter estimation. We investigate the limits of SLIMMER concerning the following questions. How accurately can the positions of two closely spaced scatterers be estimated? What is the closest distance of two scat- terers such that they can be separated with a detection rate of 50% by assuming a uniformly distributed phase difference? How many acquisitions N are required for a robust estimation (i.e., for separating two scatterers spaced by one Rayleigh resolution unit with a probability of 90%)? For all of these questions, we provide numerical results, simulations, and analytical approxima- tions. Although we take TomoSAR as the preferred application, the SLIMMER algorithm and our results on SR are generally applicable to sparse spectral estimation, including SR SAR focus- ing of point-like objects. Our results are approximately applicable to nonlinear least-squares estimation, and hence, although it is derived experimentally, they can be considered as a fundamental bound for SR of spectral estimators. We show that SR factors are in the range of 1.5-25 for the aforementioned parameter ranges of N and SNR.

Dokumentart:Zeitschriftenbeitrag
Titel:Super-resolution power and robustness of compressive sensing for spectral estimation with application to spaceborne tomographic SAR
Autoren:
AutorenInstitution oder E-Mail-Adresse der Autoren
Zhu, Xiao XiangDLR,TUM
Bamler, RichardDLR,TUM
Datum:Januar 2012
Erschienen in:IEEE Transactions on Geoscience and Remote Sensing
Referierte Publikation:Ja
In Open Access:Nein
In SCOPUS:Ja
In ISI Web of Science:Ja
Band:50
DOI :10.1109/TGRS.2011.2160183
Seitenbereich:Seiten 1-12
Verlag:IEEE
ISSN:0196-2892
Status:veröffentlicht
Stichwörter:super-resolution, SL1MMER, SAR, SAR Tomography
HGF - Forschungsbereich:Luftfahrt, Raumfahrt und Verkehr
HGF - Programm:Raumfahrt
HGF - Programmthema:Erdbeobachtung
DLR - Schwerpunkt:Raumfahrt
DLR - Forschungsgebiet:R EO - Erdbeobachtung
DLR - Teilgebiet (Projekt, Vorhaben):R - Vorhaben hochauflösende Fernerkundungsverfahren
Standort: Oberpfaffenhofen
Institute & Einrichtungen:Institut für Methodik der Fernerkundung > SAR-Signalverarbeitung
Hinterlegt von: Yuanyuan Wang
Hinterlegt am:07 Sep 2011 14:27
Letzte Änderung:13 Jul 2013 11:56

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