Direct imaging for extended targets (1 Sound-soft target ( Dirichlet boundary condition D(x)+k2(x)=0,x蜊C?i l(x)=-l(x),x味W ku÷?0.asr (過两科学大季 A Direct Numerical Imaging Method 11 National University of Defense Technology
A Direct Numerical Imaging Method Direct imaging for extended targets 11 (1) Sound-soft target (Dirichlet boundary condition) 2 ( ) ( ) 0, ( ) ( ), s s C d s i u k u u u ìï D + = 蜽 ? ïï í ï ï = - 味 W ïî x x x ¡ x x x 1 2 0, . m u r iku as r r - 骣ç ¶ ÷ ç ÷ ç ÷ ç桫¶ ÷ x
Direct imaging for extended targets From greens formula we have aGD(a, y) du aGp(a, y) ar The scattered wave received at x is Go(y, ai aG D(i, y)dy Go(ei, y aGD(aj, y) The response matrix can be written as 0(y) 9 ag(y) aGD(a1, y) aGD(N, y) T 0(y)=Go(x1,y) N, y h 防科学时太季 A Direct Numerical Imaging Method 12 National University of Defense Technology
A Direct Numerical Imaging Method Direct imaging for extended targets 12 From Greens formula we have The scattered wave received at xj is The response matrix can be written as
Direct imaging for extended targets Imaging function g(c Where the shape space V=span(vi,v2,,VMlthe leading SVs) the noise space VN: the orthogonal complement of vs (過两科学大季 A Direct Numerical Imaging Method National University of Defense Technology
A Direct Numerical Imaging Method Direct imaging for extended targets 13 Imaging function 2 1 ( ) ( ) N V I x P g = v x where • the shape space VS = span{v1 ,v2 ,…,vM}(the leading SVs) • the noise space VN: the orthogonal complement of VS
Direct imaging for extended targets (2 Sound-hard target (Neumann boundary condition) The scattered field is GN(, y)dy The scattered wave received at x is 0C0(y,x) N(aj, y)dy on The response matrix is P ago(y)or g(ydy g (過两科学大季 A Direct Numerical Imaging Method 14 National University of Defense Technology
A Direct Numerical Imaging Method Direct imaging for extended targets 14 (2) Sound-hard target (Neumann boundary condition) The scattered field is The scattered wave received at xj is The response matrix is
Direct imaging for extended targets Imaging function 1()=mam1a|2-1/(P2 OvI Where the normal direction at the boundaries is unknown we use a set of fixed search directions n,at eadhipolnt and take the maximum among them (過两科学大季 A Direct Numerical Imaging Method 15 National University of Defense Technology
A Direct Numerical Imaging Method Direct imaging for extended targets 15 Imaging function where • the normal direction at the boundaries is unknown, we use a set of fixed search directions at each point and take the maximum among them. , 1,2, , l n l L = L