Signals, including signals from outside of the subspace of bandlimited signals associated with the Shannon theorem, are acquired while still providing an acceptable reconstruction. In some aspects a denoising process is used in conjunction with sparse sampling techniques. For example, a denoising process utilizing a Cadzow algorithm may be used to reduce the amount of noise associated with sampled information. In some aspects the denoising process may be iterative such that the denoising process is repeated until the samples are denoised to a sufficient degree.
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