Optical emission spectroscopy (OES) imaging is often used for diagnostics for better understanding of the underlying mechanisms of plasmas. Typical spectral images, however, contain intensity maps that are integrated along the line-of-sight. A widespread method to extract the radial information is Abel's inversion, but most approaches result in accumulation of error toward the plasma axial position, which is often the region of most interest. Here, a Fourier-transform based Abel's inversion algorithm, which spreads the error evenly across the radial profile, is optimized for OES images collected on a push-broom hyperspectral imaging system (PbHSI). Furthermore, a sub-pixel shifting (SPS) sampling protocol is employed on the PbHSI in the direction of the radial reconstruction to allow improved fidelity from the increased number of data points. The accuracy and fidelity of the protocol are characterized and optimized with a software-based 3-dimensional hyperspectral model datacube. A systematic study of the effects of varying levels of representative added noise, different noise filters, number of data points and cosine expansions used in the inversion, as well as the spatial intensity distribution shapes of the radial profile are presented. A 3D median noise filter with 3-pixel radius, a minimum of 50 points and 8 cosine expansions is needed to keep the relative root mean squared error (rRMSE) <8%. The optimized protocol is implemented for the first time on OES images of a micro-capillary dielectric barrier discharge (μDBD) source obtained via SPS PbHSI system and the extracted radial emission of different plasma species (He, N₂, N₂⁺) are shown.