Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling
for acquisition of sparse or compressible signals that can be well
approximated by just K << N elements from an N-dimensional basis.
Instead of taking periodic samples, we measure inner products with M<N
random vectors and then recover the signal via a sparsity-seeking
optimization or greedy algorithm. The standard CS theory dictates that
robust signal recovery is possible from M=O(K log(N/K)) measurements.
The implications are promising for many applications and enable the
design of new kinds of analog-to-digital converters, cameras and
imaging systems, and sensor networks.

While this represents significant progress from Nyquist-rate sampling,
in this talk, we will demonstrate that it is possible to do even
better by more fully leveraging concepts from state-of-the-art signal
compression and processing algorithms.  In many such algorithms, the
key ingredient is a more realistic signal model that goes beyond
simple sparsity by codifying the inter-dependency structure among the
signal coefficients.  We will present a new model-based CS theory
that parallels the conventional theory and provides concrete
guidelines on how to create model-based recovery algorithms with
provable performance guarantees.  To take practical advantage of the
new theory, we integrate two relevant signal models -- wavelet trees
and block sparsity -- into two state-of-the-art CS recovery algorithms
and prove that they offer robust recovery from just M=O(K)
measurements.