$\operatorname*{argmin}_\beta\{\|y-X\beta\|^2 + \lambda\|\beta\|_1$, where $X$ is orthonormal. $\beta \in \mathbb R^d$. $X = [x_1,\ldots,x_n]^T$ and $y=(y_1,\ldots,y_n)^T \in \mathbb R^n$. $X^TX=I_{d\times d}$.
I am attempting to find an expression for \beta, which solves this lasso optimazation problem for practice this was left as a bonus question. The issue I am having in solving this problem is how to deal with the L1 norm portion.
