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The resonant tunneling diode (RTD) with mesoscopic double barrier structure has recently been employed to implement compact and versatile cellular neural/nonlinear networks (CNN's) by exploiting its unique folded-back non-linear I-V and C-V characteristics. This paper describes the design of a 128×128 RTD-based CNN along with the design of feed-forward and feedback templates for executing several commonly used image processing functions. In order to verify the image processing functions of RTD-based CNN's, full-array circuit simulations have been performed by using the quantum spice simulator that was designed at the University of Michigan. Unlike some previous designs that employed imprecise PWL model of the RTD, the RTD is represented as an internal component in the quantum spice simulator by a rigorously derived and accurate physics-based model. Due to the nano-scale quantum well defined by the double barrier structure, RTD has quantized states within the quantum well while outside the well electron energy is given by the Fermi-Dirac distribution function. Hence, the I-V and C-V characteristics of the RTD have been derived from the self-consistent solution of the Schrodinger and the Poisson's equations. The stability and settling time of the RTD-based CNN arrays are also described in this paper.