Skip to main content

Table 2 Computing r 2 using the separation of variables procedure

From: Precise two-dimensional D-bar reconstructions of human chest and phantom tank via sinc-convolution algorithm

Step

Operation

1

Form the array [ u i , j ]

 

u i , j = t R exp ( z ) e − z ( x ) 4 z ¯ μ ( z ) ¯ , where z = ( z i , z j ) f o r i , j = − M , … , N .

2

Successively form the arrays

 

b . , j + = X 1 − 1 u . , j

 

t i , . + = X 2 − 1 b i , . +

3

Form the products t i , j − = G ( s i 1 , s j 2 ) t i , j +

4

Successively form the arrays

 

b i,. − = X 2 t i,. −

 

r 2 i , j = X 1 b . , j −

 

Note 1: r 2 i , j are the approximations of r 2 at sinc points (z i , z j ).

 

Note 2: In this procedure list, we used the notation b .,j  = (b −M,j , …, b N,j )T. Similar notations are used for u .,j and t i,.