# art: ART Inverse solution In PEIP: Geophysical Inverse Theory and Optimization

## Description

ART algorythm for solving sparse linear inverse problems

## Usage

 `1` ```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<[email protected]>

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27``` ```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 Jan. 20, 2018, 9:03 a.m.