# Solve Efficiently the 1D $L_1$ Regularized Least Squares Problem (Denoising / Deblurring)

How to solve a 1D Least Squares with $$L_1$$ Regularization?
I know gradient based method, I wonder how much faster / efficient I can get.

The only difference in the MM is setting $$D = I$$.
This means there is no reason to use the Matrix Inversion Lemma. Hence one need to prevent zeros in the values of $${\Lambda}_{k}$$.