  Compressed sensing is a technique to sample compressible signals below the
Nyquist rate, whilst still allowing near optimal reconstruction of the signal.
In this paper we present a theoretical analysis of the iterative hard
thresholding algorithm when applied to the compressed sensing recovery problem.
We show that the algorithm has the following properties (made more precise in
the main text of the paper)
  - It gives near-optimal error guarantees.
  - It is robust to observation noise.
  - It succeeds with a minimum number of observations.
  - It can be used with any sampling operator for which the operator and its
adjoint can be computed.
  - The memory requirement is linear in the problem size.
  - Its computational complexity per iteration is of the same order as the
application of the measurement operator or its adjoint.
  - It requires a fixed number of iterations depending only on the logarithm of
a form of signal to noise ratio of the signal.
  - Its performance guarantees are uniform in that they only depend on
properties of the sampling operator and signal sparsity.
