We study the realization of an original Cellular Nonlinear Network (CNN) using a semiconductor tunneling structure. The elementary logic cell of the proposed CNN consists of a couple of resonant tunneling diodes (RTD) connected in series through a quantum dot. The local interconnections between the nano-cells are achieved via the tunneling in the quantum dot layer. The use of tunneling effects for interconnection resolves the problem of nano-wiring and allows us to enhance the network's computing abilities (realize a number of logic functions in one module). Based on approximate tunneling characteristics, examples of image processing are simulated.