Control oriented identification of Wiener systems is known to be a generically NP-hard problem, even in cases where the nonlinearity is known. While convex relaxations of the problem are available, these are also computationally intensive, since they typically require either solving a large number of Linear Programs or solving large-sized Semi-Definite Programs. To circumvent this difficulty, in this paper we present an alternative, based on a combining properties of interval matrices with atomic norm minimization and mixed binary programming. As illustrated in the paper, this combination leads to a computationally efficient algorithm, capable of handling problems whose size challenges existing techniques.