  This paper proposes a simple adaptive sensing and group testing algorithm for
sparse signal recovery. The algorithm, termed Compressive Adaptive Sense and
Search (CASS), is shown to be near-optimal in that it succeeds at the lowest
possible signal-to-noise-ratio (SNR) levels, improving on previous work in
adaptive compressed sensing. Like traditional compressed sensing based on
random non-adaptive design matrices, the CASS algorithm requires only k log n
measurements to recover a k-sparse signal of dimension n. However, CASS
succeeds at SNR levels that are a factor log n less than required by standard
compressed sensing. From the point of view of constructing and implementing the
sensing operation as well as computing the reconstruction, the proposed
algorithm is substantially less computationally intensive than standard
compressed sensing. CASS is also demonstrated to perform considerably better in
practice through simulation. To the best of our knowledge, this is the first
demonstration of an adaptive compressed sensing algorithm with near-optimal
theoretical guarantees and excellent practical performance. This paper also
shows that methods like compressed sensing, group testing, and pooling have an
advantage beyond simply reducing the number of measurements or tests --
adaptive versions of such methods can also improve detection and estimation
performance when compared to non-adaptive direct (uncompressed) sensing.
