TY - JOUR
T1 - Directional compactly supported box spline tight framelets with simple geometric structure
AU - Han, Bin
AU - Li, Tao
AU - Zhuang, Xiaosheng
PY - 2019/5
Y1 - 2019/5
N2 - A directional compactly supported d-dimensional Haar tight framelet is constructed such that all its high-pass filters in its underlying tight framelet filter bank have only two nonzero coefficients with opposite signs and they exhibit totally (3d−1)∕2 directions in dimension d. Furthermore, applying the projection method to such a tight framelet, a directional compactly supported box spline tight framelet with simple geometric structure is built such that all the high-pass filters in its underlying tight framelet filter bank have only two nonzero coefficients with opposite signs as well. Moreover, such compactly supported box spline tight framelets can achieve arbitrarily high numbers of directions by using refinable box splines with increasing supports. Their application to pMRI with good performance is presented.
AB - A directional compactly supported d-dimensional Haar tight framelet is constructed such that all its high-pass filters in its underlying tight framelet filter bank have only two nonzero coefficients with opposite signs and they exhibit totally (3d−1)∕2 directions in dimension d. Furthermore, applying the projection method to such a tight framelet, a directional compactly supported box spline tight framelet with simple geometric structure is built such that all the high-pass filters in its underlying tight framelet filter bank have only two nonzero coefficients with opposite signs as well. Moreover, such compactly supported box spline tight framelets can achieve arbitrarily high numbers of directions by using refinable box splines with increasing supports. Their application to pMRI with good performance is presented.
KW - Directional tight framelets
KW - Haar refinable functions
KW - Refinable box splines
KW - Tight framelet filter banks
UR - http://www.scopus.com/inward/record.url?scp=85059663176&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85059663176&origin=recordpage
U2 - 10.1016/j.aml.2018.12.016
DO - 10.1016/j.aml.2018.12.016
M3 - RGC 21 - Publication in refereed journal
SN - 0893-9659
VL - 91
SP - 213
EP - 219
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
ER -