Superresolution using the optimal recovery framework with automatic Generalized Cross-Validation

The optimal recovery deterministic estimation framework and a recently proposed Generalized Cross-Validation (GCV) approach are used in superresolution to perform the reconstruction of a high-resolution image from a series of low-resolution shifted images of the same scene. This method, an improved form of band-limited interpolation, incorporates knowledge of the shifts as well as of the known or desired spectral support of the resulting image. As a practical matter, the reconstruction is implemented piecewise using a block-by-block approach. The effects of noise and the sensitivity to the given data accuracy are mitigated by using regularization and a recently proposed GCV method for computing an optimal regularization parameter. The results compare favorably with established methods. The results using the GCV are comparable to those obtained using an experimentally chosen regularization parameter obtained using a direct computation of the actual reconstruction error.