TY - JOUR
T1 - Nonlinear approximation of functions in two dimensions by sums of wave packets
AU - Andersson, Fredrik
AU - Carlsson, Marcus
AU - de Hoop, Maarten V.
PY - 2010
Y1 - 2010
N2 - We consider the problem of approximating functions that arise in wave-equation imaging by sums of wave packets. Our objective is to find sparse decompositions of image functions, over a finite range of scales. We also address the naturally connected task of numerically approximating the wavefront set. We present an approximation where we use the dyadic parabolic decomposition, but the approach is not limited to only this type. The approach makes use of expansions in terms of exponentials, while developing an algebraic structure associated with the decomposition of functions into wave packets. (c) 2009 Elsevier Inc. All rights reserved.
AB - We consider the problem of approximating functions that arise in wave-equation imaging by sums of wave packets. Our objective is to find sparse decompositions of image functions, over a finite range of scales. We also address the naturally connected task of numerically approximating the wavefront set. We present an approximation where we use the dyadic parabolic decomposition, but the approach is not limited to only this type. The approach makes use of expansions in terms of exponentials, while developing an algebraic structure associated with the decomposition of functions into wave packets. (c) 2009 Elsevier Inc. All rights reserved.
KW - AAK theory in two variables
KW - Prony's method in two variables
KW - Wave packets
KW - Dyadic parabolic decomposition
KW - Nonlinear approximation
U2 - 10.1016/j.acha.2009.09.001
DO - 10.1016/j.acha.2009.09.001
M3 - Article
SN - 1096-603X
VL - 29
SP - 198
EP - 213
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
IS - 2
ER -