TY - GEN
T1 - Toeplitz block matrices in compressed sensing and their applications in imaging
AU - Sebert, Florian
AU - Zou, Yi Ming
AU - Ying, Leslie
PY - 2008
Y1 - 2008
N2 - Recent work in compressed sensing theory shows that sensing matrices whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse signal from a small number of measurements with high probability. In most medical imaging systems, the encoding matrices cannot take that form. Instead, they are Toeplitz block matrix. Motivated by this fact, we consider Toeplitz block matrices as the sensing matrices. We show that the probability of perfect reconstruction from a smaller number of filter outputs is also high if the filter coefficients are independently and identically- distributed random variable. Their applications in medical imaging is discussed. Simulation results are also shown to validate the theorem.
AB - Recent work in compressed sensing theory shows that sensing matrices whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse signal from a small number of measurements with high probability. In most medical imaging systems, the encoding matrices cannot take that form. Instead, they are Toeplitz block matrix. Motivated by this fact, we consider Toeplitz block matrices as the sensing matrices. We show that the probability of perfect reconstruction from a smaller number of filter outputs is also high if the filter coefficients are independently and identically- distributed random variable. Their applications in medical imaging is discussed. Simulation results are also shown to validate the theorem.
KW - Compressed sensing
KW - Random point spread function
KW - Toeplitz block matrix
UR - https://www.scopus.com/pages/publications/51849111547
U2 - 10.1109/ITAB.2008.4570587
DO - 10.1109/ITAB.2008.4570587
M3 - Conference contribution
AN - SCOPUS:51849111547
SN - 9781424422555
T3 - 5th Int. Conference on Information Technology and Applications in Biomedicine, ITAB 2008 in conjunction with 2nd Int. Symposium and Summer School on Biomedical and Health Engineering, IS3BHE 2008
SP - 47
EP - 50
BT - 5th Int. Conference on Information Technology and Applications in Biomedicine, ITAB 2008 in conjunction with 2nd Int. Symposium and Summer School on Biomedical and Health Engineering, IS3BHE 2008
T2 - 5th International Conference on Information Technology and Applications in Biomedicine, ITAB 2008 in conjunction with 2nd International Symposium and Summer School on Biomedical and Health Engineering, IS3BHE 2008
Y2 - 30 May 2008 through 31 May 2008
ER -