In this paper, we take a new look at real-world image super-resolution (real-SR) from a multi-task learning perspective.

Isomap is a nonlinear dimensionality reduction method and finds low-dimensional embedding of high-dimensional data by preserving the pairwise geodesic distances between data pointsinmanifold. In2-dimensional embedding manifoldM,thegeodesic polygonal curvePi,j canbeprojected on the straight line connected it two endpoints. Every line segment ofPi,j has a corresponding line segmentinthethestraightline. The hyper-parameters searched over include the dimension of node representation as well as hyper-parameters specific to each model.

Specifically,weshowthatthebound is related to the perturbation/noise level and the recovery of the true support of the leading eigenvector as well. We also investigate the estimator of SGEP via imposing a non-convex regularization. Such estimator can achieve the optimal error rate and can recover the sparsity structure as well.