Sparse signal recovery from incomplete and perturbed data

Abstract

Sparse signal recovery consists of algorithms that are able to recover undersampled high dimensional signals accurately. These algorithms require fewer measurements than traditional Shannon/Nyquist sampling theorem demands. Sparse signal recovery has found many applications including magnetic resonance imaging, electromagnetic inverse scattering, radar/sonar imaging, seismic data collection, sensor array processing and channel estimation. The focus of this thesis is on electromagentic inverse scattering problem and joint estimation of the frequency o set and the channel impulse response in OFDM. In the electromagnetic inverse scattering problem, the aim is to nd the electromagnetic properties of unknown targets from measured scattered eld. The reconstruction of closely placed point-like objects is investigated. The application of the greedy pursuit based sparse recovery methods, OMP and FTB-OMP, is proposed for increasing the reconstruction resolution. The performances of the proposed methods are compared against NESTA and MT-BCS methods. Simulations show that the FTBOMP method increases the resolution of the regular OMP and is superior to NESTA for less noisy measurements. OFDM is a multicarrier modulation technique that is very sensitive to frequency synchronization and channel estimation errors. Frequency o set destroys the orthogonality of the OFDM carriers and results in intercarrier inteference that causes severe performance degradation. A new approach that represents the channel impulse response as a 1-block sparse signal in a dictionary built by concatenating subspaces of frequency o set values is proposed. Thus the frequency o set and the channel impulse response can be jointly estimated. Only one OFDM training block is used and noise or channel statistics are not required. Its performance is close to maximum likelihood estimation and does not depend on frequency o set. v OZET EKS_IK VE BOZUK VER_ILER _ILE SEYREK S_INYAL GER_IC ATIMI Seyrek sinyal geri cat m , yuksek boyutlu sinyalleri az say da ornek uzerinden tekrar olu sturabilen yontemlerden meydana gelir. Bu yontemler ile sinyal geri cat m i cin gereksinim duyulan ornek say s , geleneksel Shannon/Nyquist ornekleme teoremine k yasla cok daha az say dad r. Seyrek sinyal geri cat m manyetik rezonans goruntuleme, elektromanyetik ters sa c l m problemi, radar/sonar goruntuleme, sismik veri toplama, sensor dizi i sleme ve kanal kestirimi olmak uzere bir cok uygulamada kullan lmaktad r. Bu tez cal smas n n oda g elektromanyetik ters sa c l m problemi ve OFDM i cin frekans kaymas n n ve kanal yan t n n birlikte kestirilmesidir. Ters sa c l m probleminde sa c lan elektromanyetik alandan hedef cisimlerin ozelliklerinin belirlenmesi ama clanmaktad r. Bu kapsamda birbirine yak n konumland r lm s nokta cisimlerin yerlerinin bulunmas incelenmi stir. Bu problemdeki geri cat m cozunurlu gunun iyile stirilmesi i cin a cgozlu geri cat m yontemlerinden dikgen uyum kovalama OMP ve esnek a ga c arama yap l FTB-OMP yontemleri onerilmi stir. Onerilen yontemlerin ba sar mlar NESTA ve MTBCS yontemleri ile kar s la st r lm st r. Yap lan benzetimler FTB-OMP yonteminin OMP geri