TY - JOUR
T1 - Stable restoration and separation of approximately sparse signals
AU - Studer, Christoph
AU - Baraniuk, Richard G.
N1 - Funding Information:
This work was supported by the Swiss National Science Foundation (SNSF) under Grant PA00P2-134155 and by the Grants NSF CCF-0431150 , CCF-0728867 , CCF-0926127 , DARPA/ONR N66001-08-1-2065 , N66001-11-1-4090 , N66001-11-C-4092 , ONR N00014-08-1-1112 , N00014-10-1-0989 , AFOSR FA9550-09-1-0432 , ARO MURIs W911NF-07-1-0185 and W911NF-09-1-0383 , and by the Texas Instruments Leadership University Program .
PY - 2014/7
Y1 - 2014/7
N2 - This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise. The algorithms and analytical recovery conditions consider varying degrees of signal and interference support-set knowledge. Particular applications covered by the proposed framework include the restoration of signals impaired by impulse noise, narrowband interference, or saturation/clipping, as well as image in-painting, super-resolution, and signal separation. Two application examples for audio and image restoration demonstrate the efficacy of the approach.
AB - This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise. The algorithms and analytical recovery conditions consider varying degrees of signal and interference support-set knowledge. Particular applications covered by the proposed framework include the restoration of signals impaired by impulse noise, narrowband interference, or saturation/clipping, as well as image in-painting, super-resolution, and signal separation. Two application examples for audio and image restoration demonstrate the efficacy of the approach.
KW - Basis-pursuit denoising
KW - Coherence
KW - Deterministic recovery guarantees
KW - Signal restoration
KW - Signal separation
KW - Sparse signal recovery
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U2 - 10.1016/j.acha.2013.08.006
DO - 10.1016/j.acha.2013.08.006
M3 - Article
AN - SCOPUS:84900558998
SN - 1063-5203
VL - 37
SP - 12
EP - 35
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
IS - 1
ER -