Numerical error analysis for super-resolution reconstruction

Superresolution reconstruction (SR) is a technique for reconstructing a high resolution image from several low resolution ones. Recently, some researchers study the relationship of SR error and magnification factor, and give out the efficient and forbidden magnification range in their published literature. Based on their work, we describe SR error bound in more explicit way and reveal the essential factor affecting SR performance, if infinite low resolution (LR) observations are given. For SR implementation, smooth regularization serves as an efficient tool for producing stable SR solution, but this operator degrades SR performance and produces overly smooth SR image at certain magnifications. To show its mechanism, we augment SR model by integrating regularization operator into it, and then present the curve of SR error bound vs magnification factors. It is proven that the forbidden magnification range no longer exists when the regularization is involved.