TY - JOUR
T1 - Iterative hard thresholding for compressed sensing
AU - Blumensath, T.
AU - Davies, M.E.
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
KW - Algorithms
KW - Compressed sensing
KW - Sparse inverse problem
KW - Signal recovery
KW - Iterative hard thresholding
UR - http://www.scopus.com/inward/record.url?scp=69949164527&partnerID=8YFLogxK
U2 - 10.1016/j.acha.2009.04.002
DO - 10.1016/j.acha.2009.04.002
M3 - Article
VL - 27
SP - 265
EP - 274
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
SN - 1063-5203
IS - 3
ER -