Sampling theory has benefited from a surge of research in recent years. In this talk we present several extensions of the Shannon theorem, which treat a wide class of input signals as well as nonideal sampling, nonlinear distortions, and constrained recovery procedures. This framework is based on an optimization viewpoint, which takes into account both the goodness of fit of the reconstructed signal to the given samples, as well as relevant prior knowledge on the original signal. As we show, using appropriate optimization tools, we can develop recovery procedures for a wide class of sampling techniques. In addition, we illustrate how these methods can be used in combination with compressed sensing algorithms to recover various classes of structured analog signals from sub-Nyquist samples.
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