Compressed sensing of analog signals in shift-invariant spaces
IEEE Transactions on Signal Processing
Block sparsity and sampling over a union of subspaces
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
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We study a sampling setup where a continuous-time signal is mapped by a memoryless, invertible and nonlinear transformation, and then sampled in a nonideal manner. Such scenarios appear, for example, in acquisition systems where a sensor introduces static nonlinearity, before the signal is sampled by a practical analog-to-digital converter. We develop the theory and a concrete algorithm to perfectly recover a signal within a subspace, from its nonlinear and nonideal samples. Three alternative formulations of the algorithm are described that provide different insights into the structure of the solution: A series of oblique projections, approximated projections onto convex sets, and quasi-Newton iterations. Using classical analysis techniques of descent-based methods, and recent results on frame perturbation theory, we prove convergence of our algorithm to the true input signal. We demonstrate our method by simulations, and explain the applicability of our theory to Wiener-Hammerstein analog-to-digital hybrid systems.