Information theoretic performance limits (ECE 592 Module 48)

To move toward optimal sparse recovery, we start by defining a framework for which we will provide an optimal signal recovery system. One of our goals in this framework will be to minimize the number of measurements. We will also consider measurement noise, because the measurement process is often analog; in particular, we will assume that the noise is Gaussian. Our signal model involves a sparse signal that is nonzero with probability epsilon, in which case the signal entry adheres to some iid pdf. Finally, the measurement matrix will be i.i.d., where each of its columns will have unit norm, on average. For this setting, a preliminary information theoretic result was provided in 2006. This result interpreted a compressed sensing system as analogous to a communication system, where compressed sensing measurement and reconstruction are analogous to the encoder and decoder of a communication system. This result was a bound on best-possible signal recovery quality, and follow-up modules will move toward a precise understanding of performance limits for compressed sensing recovery.