  The principal rank-one (RO) components of an image represent the
self-similarity of the image, which is an important property for image
restoration. However, the RO components of a corrupted image could be decimated
by the procedure of image denoising. We suggest that the RO property should be
utilized and the decimation should be avoided in image restoration. To achieve
this, we propose a new framework comprised of two modules, i.e., the RO
decomposition and RO reconstruction. The RO decomposition is developed to
decompose a corrupted image into the RO components and residual. This is
achieved by successively applying RO projections to the image or its residuals
to extract the RO components. The RO projections, based on neural networks,
extract the closest RO component of an image. The RO reconstruction is aimed to
reconstruct the important information, respectively from the RO components and
residual, as well as to restore the image from this reconstructed information.
Experimental results on four tasks, i.e., noise-free image super-resolution
(SR), realistic image SR, gray-scale image denoising, and color image
denoising, show that the method is effective and efficient for image
restoration, and it delivers superior performance for realistic image SR and
color image denoising.
