art: ART Inverse solution

In PEIP: Geophysical Inverse Theory and Optimization

ART Inverse solution

Description

ART algorythm for solving sparse linear inverse problems

Usage

art(A, b, tolx, maxiter)

Arguments

A	Constraint matrix
b	right hand side
tolx	difference tolerance for successive iterations (stopping criteria)
maxiter	maximum iterations (stopping criteria).

Details

Alpha is a damping factor. If alpha<1, then we won't take full steps in the ART direction. Using a smaller value of alpha (say alpha=.75) can help with convergence on some problems.

Value

x

solution

Author(s)

Jonathan M. Lees<[e-mail]>

References

Aster, R.C., C.H. Thurber, and B. Borchers, Parameter Estimation and Inverse Problems, Elsevier Academic Press, Amsterdam, 2005.

Examples

set.seed(2015)
G = setDesignG()
### % Setup the true model.
mtruem=matrix(rep(0, 16*16), ncol=16,nrow=16);

mtruem[9,9]=1; mtruem[9,10]=1; mtruem[9,11]=1;
mtruem[10,9]=1; mtruem[10,11]=1;
mtruem[11,9]=1; mtruem[11,10]=1; mtruem[11,11]=1;
mtruem[2,3]=1; mtruem[2,4]=1;
mtruem[3,3]=1; mtruem[3,4]=1;

### % reshape the true model to be a vector
mtruev=as.vector(mtruem);

### % Compute the data.
dtrue=G %*% mtruev;

### % Add the noise.


d=dtrue+0.01*rnorm(length(dtrue));

mkac<-art(G,d,0.01,200)
par(mfrow=c(1,2))
imagesc(matrix(mtruem,16,16) , asp=1 , main="True Model" );

imagesc(matrix(mkac,16,16) , asp=1 , main="ART Solution" );

PEIP documentation built on Aug. 21, 2023, 9:10 a.m.