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. In some aspects, the denoising process converts a set of received samples into another set corresponding to a signal with a Finite Rate of Innovation (FRI), or to an approximation of such a signal. The disclosure relates in some aspects to combination of a denoising process with annihilating filter methods to retrieve information from a noisy, sparse sampled signal. The disclosure relates in some aspects to determining a sampling kernel to be used to sample the signal based on noise associated with the signal. The disclosure relates in some aspects to determining the number of samples to obtain from a signal over a period of time based on noise associated with the signal. The disclosure relates in some aspects to determining the finite number of innovations of a received signal.
展开▼
