  Self-similarity learning has been recognized as a promising method for single
image super-resolution (SR) to produce high-resolution (HR) image in recent
years. The performance of learning based SR reconstruction, however, highly
depends on learned representation coeffcients. Due to the degradation of input
image, conventional sparse coding is prone to produce unfaithful representation
coeffcients. To this end, we propose a novel kernel based low-rank sparse model
with self-similarity learning for single image SR which incorporates
nonlocalsimilarity prior to enforce similar patches having similar
representation weights. We perform a gradual magnification scheme, using
self-examples extracted from the degraded input image and up-scaled versions.
To exploit nonlocal-similarity, we concatenate the vectorized input patch and
its nonlocal neighbors at different locations into a data matrix which consists
of similar components. Then we map the nonlocal data matrix into a
high-dimensional feature space by kernel method to capture their nonlinear
structures. Under the assumption that the sparse coeffcients for the nonlocal
data in the kernel space should be low-rank, we impose low-rank constraint on
sparse coding to share similarities among representation coeffcients and remove
outliers in order that stable weights for SR reconstruction can be obtained.
Experimental results demonstrate the advantage of our proposed method in both
visual quality and reconstruction error.
