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In this paper, we analyze and design a new type of diffusion process that denoises and sharpens images for resolution enhancement of passive millimeter wave images, simultaneously. In this algorithm, a coupled shock-diffusion filter is designed, where, according to image features such as edges, textures, and fine parts, it performs a forward smoothing along the tangent direction to the isophote lines, a backward sharpening along the normal directions, or only an isotropic diffusion, respectively. A qualitative evaluation of this algorithm is illustrated with simulated data as well as imaging results from the passive millimeter-wave imaging system in 91.5 GHz. Experimental results demonstrate that our algorithm can substantially enhance image features on denoising image.