TY - GEN
T1 - Deterministic Matrices with a Restricted Isometry Property for Partially Structured Sparse Signals
AU - Kaplan, Alihan
AU - Pohl, Volker
AU - Boche, Holger
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/7
Y1 - 2019/7
N2 - Compressive sampling has become an important tool in diverse applications. One of its main challenges, the construction of deterministic sensing matrices with restricted isometry property (RIP) in the optimal sparsity regime, is still an open problem, despite being of crucial importance for practical system designs. The only known work constructing deterministic RIP matrices beyond the square root bottleneck is due to Bourgain et al. The aim of this paper is to construct sensing matrices consisting of two orthogonal bases and to analyse their RIP properties based on the flat-RIP. Using a known estimation on exponential sums due to Karatsuba, we deduce an RIP result for signals which are restricted to a certain sparse structure. Without any assumption on the sparsity structure, we end up facing a known open problem from number theory regarding exponential sums.
AB - Compressive sampling has become an important tool in diverse applications. One of its main challenges, the construction of deterministic sensing matrices with restricted isometry property (RIP) in the optimal sparsity regime, is still an open problem, despite being of crucial importance for practical system designs. The only known work constructing deterministic RIP matrices beyond the square root bottleneck is due to Bourgain et al. The aim of this paper is to construct sensing matrices consisting of two orthogonal bases and to analyse their RIP properties based on the flat-RIP. Using a known estimation on exponential sums due to Karatsuba, we deduce an RIP result for signals which are restricted to a certain sparse structure. Without any assumption on the sparsity structure, we end up facing a known open problem from number theory regarding exponential sums.
KW - deterministic compressive sampling
KW - flat restricted isometry property
KW - structured sparsity
UR - http://www.scopus.com/inward/record.url?scp=85082859115&partnerID=8YFLogxK
U2 - 10.1109/SampTA45681.2019.9030945
DO - 10.1109/SampTA45681.2019.9030945
M3 - Conference contribution
AN - SCOPUS:85082859115
T3 - 2019 13th International Conference on Sampling Theory and Applications, SampTA 2019
BT - 2019 13th International Conference on Sampling Theory and Applications, SampTA 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 13th International Conference on Sampling Theory and Applications, SampTA 2019
Y2 - 8 July 2019 through 12 July 2019
ER -