Adaptive refinement and noise reduction methods for sparse signal reconstruction
The Iterative Re-Weighted (IRW) algorithm is tested as a solver for the maximum sparseness constraint underdetermined linear inverse problem. The pseudoinverse of the A-Matrix for this problem is formulated and tested using the QR decomposition and the SVD methods to compute it. To improve the resolution of the peaks obtained in the spectrum, we use an Adaptive refinement method because this is computationally more efficient than increasing the uniform frequency grid. Two methods are formulated and tested to reduce the effect of noise when the signal is corrupted by additive white Gaussian noise (AWGN). They are, namely, the Regularization and the SVD Truncation methods. Regularization is successful in reducing the noise components in the IRW solution. The SVD Truncation method is unsuccessful in removing the noise. We use Regularization and Refinement to form the composite methods namely Ref_Reg (first refinement then regularization) and Reg_Ref (opposite order) which are used to improve the resolution and to remove the noise components when a signal with off-grid frequency components is corrupted by noise. (Abstract shortened by UMI.)
Malladi, Suresh, "Adaptive refinement and noise reduction methods for sparse signal reconstruction" (2004). ETD Collection for University of Texas, El Paso. AAIEP10580.