"Frame Multipliers and Compressive Sensing"Tauböck, GeorgWe investigate the applicability of finite frame multipliers as measurement matrices in compressive sensing. In particular, we present several theoretical results regarding the uniqueness of the solution of sparse reconstruction. For example, we show that subsampled frame multipliers are full spark for almost all multiplier symbols provided that the involved frames are full spark and their cardinalities are sufficiently large. This includes Fourier and Gabor multipliers (for almost all windows) as special cases. Moreover, our uniqueness results extend to sparsity with respect to linear and nonlinear dictionaries. Numerical experiments confirm that this novel class of structured measurement matrices provides excellent reconstruction performance in compressive sensing scenarios. This is joint work with Shristi Rajbamshi and Peter Balazs. |
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