Typical $l_1$-recovery limit of sparse vectors represented by concatenations of random orthogonal matrices

Yoshiyuki Kabashima, Mikko Vehkapera, Saikat Chatterjee

We consider the problem of recovering an $N$-dimensional sparse vector $\vm{x}$ from its linear transformation $\vm{y}=\vm{D} \vm{x}$ of $M(<N)$ dimension. Minimizing the $l_1$-…