This study aims to enhance spectral resolution in Fourier transform infrared spectroscopy (FTIR), a crucial element for in-depth molecular analysis in clinical diagnosis. We address this challenge by developing spectral super-resolution models based on residual networks and U-Net (SSR-ResUNet), incorporating 1D, 2D, and 3D CNNs to reconstruct an image equivalent to a high-resolution IR spectral image recorded at a spectral resolution of 2 cm-1 from a low-resolution IR spectral image acquired at a resolution of 16 cm-1. Trained and tested on real FTIR images acquired from renal graft tissue sections, our deep-learning-based models achieved very good performance in terms of root-mean-square error (RMSE) and structural similarity index metric (SSIM), surpassing traditional linear and cubic interpolation while delivering similar results in terms of the retrieval of spatial histological structures obtained through K-means clustering. Our spectral super-resolution approach offers an efficient solution to overcome the limitations of IR image acquisition time, enabling a reduction in an acquisition time of up to 87.5% while preserving similar spectral quality. These advancements pave the way for faster infrared spectral imaging acquisitions while preserving the molecular information contained in high-resolution spectra, which is an important step toward future clinical applications.