Sparse Signal Recovery From Incomplete And Perturbed Data

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 offset and the channel impulse response in OFDM. In the electromagnetic inverse scattering problem, the aim is to find the electromagnetic properties of unknown targets from measured scattered field. 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 FTB-OMP 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 offset 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 offset values is proposed. Thus the frequency offset 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 offset.