  Oversampled adaptive sensing (OAS) is a Bayesian framework recently proposed
for effective sensing of structured signals in a time-limited setting. In
contrast to the conventional blind oversampling, OAS uses the prior information
on the signal to construct posterior beliefs sequentially. These beliefs help
in constructive oversampling which iteratively evolves through a sequence of
time sub-frames.
  The initial studies of OAS consider the idealistic assumption of full control
on sensing coefficients which is not feasible in many applications. In this
work, we extend the initial investigations on OAS to more realistic settings in
which the sensing coefficients are selected from a predefined set of possible
choices, referred to as the codebook. We extend the OAS framework to these
settings and compare its performance with classical non-adaptive approaches.
