It is still obtained, providing the restored signals are acceptable, including signals from outside of the subspace of the band-limited signals associated with the Shannon theorem. In some aspects, the denoising process is used with a sparse sampling technique. For example, a denoising process using a CAD algorithm jaws may be used to reduce the amount of noise associated with sampled information. In some aspect, the denoising process may be iterative such that the denoising process is repeated until enough samples are easing Dino sufficient. In some aspect, the denoising process is converted into another set corresponding to the approximation of the signal with a rate Innovation (FRI) to a finite set of received samples, or those signals. The disclosure further relates to the combination of filter extinction method with denoising process for retrieving information from the noisy signal at a sampling rare of some aspects. This disclosure relates to determining a sampling kernel to be used to sample the signal based on noise associated with the signal in some embodiments. This disclosure relates to determining the number of samples to obtain from a signal over a period of time based on noise associated with the signal in some embodiments. This disclosure relates to determining the finite number of innovations of a received signal in some aspects.
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