Inverse filters associated with polynomials of multiple graph shifts and Wiener filters have been widely used in denoising deterministic and (wide-band) stationary graphs, non-subsampled filter banks and signal reconstruction, and many other applications. In this talk, we consider distributed algorithms to implement inverse filtering procedure and Wiener filtering procedure on networks in which agents are equipped with a data processing subsystem for limited data storage and computation power, and with a one-hop communication subsystem for direct data exchange only with their adjacent agents.