ICORE is a command-line driven co-addition, mosaicking, and resolution enhancement (HiRes) tool for creating science quality products from image data in FITS format and with World Coordinate System information following the FITS-WCS standard. It includes preparatory steps such as image background matching, photometric gain-matching, and pixel-outlier rejection. Co-addition and/or HiRes'ing can be performed in either the inertial WCS or in the rest frame of a moving object. Three interpolation methods are supported: overlap-area weighting, drizzle, and weighting by the detector Point Response Function (PRF). The latter enables the creation of matched-filtered products for optimal point-source detection, but most importantly allows for resolution enhancement using a spatially-dependent deconvolution method. This is a variant of the classic Richardson-Lucy algorithm with the added benefit to simultaneously register and co-add multiple images to optimize signal-to-noise and sampling of the instrumental PSF. It can assume real (or otherwise "flat") image priors, mitigate "ringing" artifacts, and assess the quality of image solutions using statistically-motivated convergence criteria. Uncertainties are also estimated and internally validated for all products. The software supports multithreading that can be configured for different architectures. Numerous example scripts are included (with test data) to co-add and/or HiRes image data from Spitzer-IRAC/MIPS, WISE, and Herschel-SPIRE.