Randomized linear regression

Let $\mathbf{\Pi}$ be a properly scaled JL matrix (random , sparse random etc.) with $m=O(\frac{d}{\epsilon^2})$ rows¹. Then with probability $9/10$, for any $\mathbf{A} \in \mathbb{R}^{n \times d}$ and $\mathbf{b} \in \mathbb{R}^n$, $$\lVert \mathbf{A}\tilde{\mathbf{x}}-\mathbf{b}\rVert_2^2 \leq (1+\epsilon)\lVert \mathbf{A}\mathbf{x}^*-\mathbf{b}\rVert_2^2$$ where $\tilde{\mathbf{x}} = \arg\min_\mathbf{x}\lVert \mathbf{\Pi Ax}-\mathbf{\Pi b}\rVert_2^2$.