ART Inverse solution
ART algorythm for solving sparse linear inverse problems
art(A, b, tolx, maxiter)
A |
Constraint matrix |
b |
right hand side |
tolx |
difference tolerance for successive iterations (stopping criteria) |
maxiter |
maximum iterations (stopping criteria). |
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.
x |
solution |
Jonathan M. Lees<jonathan.lees@unc.edu>
Aster, R.C., C.H. Thurber, and B. Borchers, Parameter Estimation and Inverse Problems, Elsevier Academic Press, Amsterdam, 2005.
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" );
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