Recently there has been a significant interest in reconstructing a high-resolution (HR) image based on a set of low-resolution (LR) images with relative displacement. These images are typically undersampled with respect to the image spectrum of a HR image. I show that, although ideally a resolution increase of N times is possible with N LR images, in a practical system noise is a limiting factor that increases substantially as we approach this theoretical superresolution limit. For one dimension and a special case with two LR images, I present an analytical result of the noise amplification as a function of their displacement. This is defined as a condition number of the superresolution system, with the associated definitions of a well-conditioned and ill-conditioned superresolution reconstruction system.
© 2003 Optical Society of America
(100.1830) Image processing : Deconvolution
(100.2000) Image processing : Digital image processing
(100.3020) Image processing : Image reconstruction-restoration
(100.6640) Image processing : Superresolution
(110.4280) Imaging systems : Noise in imaging systems
Edmund Y. Lam, "Noise in superresolution reconstruction," Opt. Lett. 28, 2234-2236 (2003)