Push-broom hyperspectral imaging (Pb-HSI) is a powerful technique for obtaining the spectral information along with the spatial information simultaneously for various applications, from remote sensing to chemical imaging. Spatial resolution improvement is beneficial in many instances; however, typical solutions suffer from the limitation of geometric extent, lowered light throughput, or reduced field-of-view (FOV). Sub-pixel shifting (SPS) acquires higher-resolution images, compared to typical imaging approaches, from the deconvolution of low-resolution images acquired with a higher sampling rate. Furthermore, SPS is particularly suited for Pb-HSI due to its scanning nature. In this study, an SPS approach is developed and implemented on a Pb-HSI system for plasma optical emission spectroscopy. The preliminary results showed that a periodic deconvolution error was generated in the final SPS Pb-HSI images. The periodic error was traced back to random noise present in the raw/convoluted SPS data and its frequency displays an inverse relationship with the number of sub-pixel samples acquired. Computer modelled data allows studying the effect of varying the relative standard deviation (RSD) in the raw/convoluted SPS data on the final reconstructed SPS images and optimization of noise filtering. The optimized SPS Pb-HSI technique was used to acquire the line-of-sight integrated optical emission maps from an atmospheric pressure micro-capillary dielectric barrier discharge (μDBD). The selected plasma species of interest (He, I, N2, N2 +, and O) yield some insight into the underlying mechanisms. The SPS Pb-HSI technique developed here will allow implementing geometric super-resolution in many applications, for example, it will be used for extracting radially resolved information from Abel's inversion protocols, where improved fitting is expected due to the increase in resolution/data points.