L1 least squares with sparsity
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)
irlsl1reg(G, d, L, alpha, maxiter = 100, tolx = 1e-04, tolr = 1e-06)
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 |
m |
model vector |
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.
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" );
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.