Abstract
A combinatorial framework for the construction of measurement matrices for compressive sensing is shown to exhibit great flexibility in signal recovery. The deterministic column replacement technique is hierarchical: Given as input a pattern matrix and ingredient measurement matrices, it produces a larger measurement matrix by replacing elements of the pattern matrix with columns from the ingredient matrices. Recovery for the measurement matrix produced does not rely on any fixed algorithm; rather it employs the recovery schemes of the ingredient matrices, which may differ from ingredient to ingredient. Because ingredient matrices can be much smaller than the measurement matrix produced, one can employ more computationally intensive recovery methods, sometimes resulting in fewer measurements. Noise can be accommodated in signal recovery by imposing additional conditions both on the pattern matrix and on the ingredient measurement matrices.
| Original language | English (US) |
|---|---|
| Journal | Discrete Applied Mathematics |
| DOIs | |
| State | Accepted/In press - 2017 |
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Keywords
- Compressive sensing
- Deterministic column replacement
- Hash family
- Hierarchical signal recovery
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics
Cite this
A hierarchical framework for recovery in compressive sensing. / Colbourn, Charles; Horsley, Daniel; Syrotiuk, Violet.
In: Discrete Applied Mathematics, 2017.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A hierarchical framework for recovery in compressive sensing
AU - Colbourn, Charles
AU - Horsley, Daniel
AU - Syrotiuk, Violet
PY - 2017
Y1 - 2017
N2 - A combinatorial framework for the construction of measurement matrices for compressive sensing is shown to exhibit great flexibility in signal recovery. The deterministic column replacement technique is hierarchical: Given as input a pattern matrix and ingredient measurement matrices, it produces a larger measurement matrix by replacing elements of the pattern matrix with columns from the ingredient matrices. Recovery for the measurement matrix produced does not rely on any fixed algorithm; rather it employs the recovery schemes of the ingredient matrices, which may differ from ingredient to ingredient. Because ingredient matrices can be much smaller than the measurement matrix produced, one can employ more computationally intensive recovery methods, sometimes resulting in fewer measurements. Noise can be accommodated in signal recovery by imposing additional conditions both on the pattern matrix and on the ingredient measurement matrices.
AB - A combinatorial framework for the construction of measurement matrices for compressive sensing is shown to exhibit great flexibility in signal recovery. The deterministic column replacement technique is hierarchical: Given as input a pattern matrix and ingredient measurement matrices, it produces a larger measurement matrix by replacing elements of the pattern matrix with columns from the ingredient matrices. Recovery for the measurement matrix produced does not rely on any fixed algorithm; rather it employs the recovery schemes of the ingredient matrices, which may differ from ingredient to ingredient. Because ingredient matrices can be much smaller than the measurement matrix produced, one can employ more computationally intensive recovery methods, sometimes resulting in fewer measurements. Noise can be accommodated in signal recovery by imposing additional conditions both on the pattern matrix and on the ingredient measurement matrices.
KW - Compressive sensing
KW - Deterministic column replacement
KW - Hash family
KW - Hierarchical signal recovery
UR - http://www.scopus.com/inward/record.url?scp=85033775257&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85033775257&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2017.10.004
DO - 10.1016/j.dam.2017.10.004
M3 - Article
AN - SCOPUS:85033775257
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
ER -