Handbook of Biomedical Optics

Inverse Models of Light Transport 347

in a subspace of relatively low dimension. Deriving the Krylov

sequences for the problems (17.89) or (17.91), both give rise to

the same set







  







…

 

K

α

α α= +

=

∑

A A AA A A

T T T T T

y y y, , ,

j

j

j

0

AA A

( )

=

−j j





…

 

…

T

y

:{ , , ,

( ) ( )

υ υ

α α

0 1



…υ

α

( )

}

j

(17.99)

is basis set is clearly a linear combination of the basis for the

unregularized Krylov space of dimension J given by







…K ≡ =

( )

= −

{ }

{ }: , ,

( )

υ

j

j

j JA

~

A

~

A

~

T T

y 0 1

(17.100)

which implies that the Krylov spaces spanned by (17.99) and

(17.100) are the same. Finally, we may construct the Krylov space

for the original parameters:

K

α

α

α α

υ