A novel theoretical analysis on optimal pipeline of multi-frame image super-resolution using sparse coding

Super-resolution is the process of obtaining a high-resolution (HR) image from one or more low-resolution (LR) images. Single image super-resolution (SISR) deals with one LR image while multi-frame super-resolution (MFSR) employs several LR ones to reach the HR output. MFSR pipeline consists of alignment, fusion, and reconstruction. We conduct a theoretical analysis using sparse coding (SC) and iterative shrinkage-thresholding algorithm to fill the gap of mathematical justification in the execution order of the optimal MFSR pipeline. Our analysis recommends executing alignment and fusion before the reconstruction stage (whether through deconvolution or SISR techniques). The suggested order ensures enhanced performance in terms of peak signal-to-noise ratio and structural similarity index. The optimal pipeline also reduces computational complexity compared to intuitive approaches that apply SISR to each input LR image. Also, we demonstrate the usefulness of SC in analysis of computer vision tasks such as MFSR, leveraging the sparsity assumption in natural images. Simulation results support the findings of our theoretical analysis, both quantitatively and qualitatively.