After eight months of continuous observations, the Wide-field Infrared Survey Explorer (WISE) mapped the entire sky at 3.4 {mu}m, 4.6 {mu}m, 12 {mu}m and 22 {mu}m. We have begun a dedicated WISE High Resolution Galaxy Atlas (WHRGA) project to fully characterize large, nearby galaxies and produce a legacy image atlas and source catalogue. Here we summarize the deconvolution technique used to significantly improve the spatial resolution of WISE imaging, specifically designed to study the internal anatomy of nearby galaxies. As a case study, we present results for the galaxy NGC 1566, comparing the WISE super-resolution image processing to that of Spitzer, GALEX and ground-based imaging. The is the first paper in a two part series; results for a much larger sample of nearby galaxies is presented in the second paper.