We proposed to apply compressed sensing to realize information sharing of link quality for wireless mesh networks (WMNs) with grid topology. In this paper, we extend the link quality sharing method to be applied for WMNs with arbitrary topology. For arbitrary topology WMNs, we introduce a link quality matrix and a matrix formula for compressed sensing. By employing a diffusion wavelets basis, the link quality matrix is converted to its sparse equivalent. Based on the sparse matrix, information sharing is achieved by compressed sensing. In addition, we propose compressed transmission for arbitrary topology WMNs, in which only the compressed link quality information is transmitted. Experiments and simulations clarify that the proposed methods can reduce the amount of data transmitted for information sharing and maintain the quality of the shared information.