# irlsl1reg: L1 least squares with sparsity In PEIP: Geophysical Inverse Theory and Optimization

## Description

Solves the system Gm=d using sparsity regularization on Lm. Solves the L1 regularized least squares problem: min norm(G*m-d,2)^2+alpha*norm(L*m,1)

## Usage

 `1` ```irlsl1reg(G, d, L, alpha, maxiter = 100, tolx = 1e-04, tolr = 1e-06) ```

## Arguments

 `G` design matrix `d` right hand side `L` regularization matrix `alpha` regularization parameter `maxiter` Maximum number of IRLS iterations `tolx` Tolerance on successive iterates `tolr` Tolerance below which we consider an element of L*m to be effectively zero

## Value

 `m` model vector

## 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``` ```n = 20 G = shawG(n,n) spike = rep(0,n) spike[10] = 1 spiken = G %*% spike wts = rep(1, n) delta = 1e-03 set.seed(2015) dspiken = spiken + 6e-6 *rnorm(length(spiken)) L1 = get_l_rough(n,1); alpha = 0.001 k = irlsl1reg(G, dspiken, L1, alpha, maxiter = 100, tolx = 1e-04, tolr = 1e-06) plotconst(k,-pi/2,pi/2, ylim=c(-.2, 0.5), xlab="theta", ylab="Intensity" ); ```

PEIP documentation built on Jan. 20, 2018, 9:03 a.m.