Subspace learning refers to the technique of finding a subspace Rm embedded in a high dimensional space Rn (n > m).
Ma et al. (2009, 2010a,b) proposed a position-based FH method that borrowed the idea of neighbor embedding. After dividing all images into patches, the high-resolution counterpart of a given input low-resolution image patch is estimated by applying neighbor embedding to those training image patches located in the same position as the test patch. The authors also applied the position-based FH method to multi-view FH in which a multi-view face synthesis procedure was conducted before hallucination by utilizing a method similar to neighbor embedding (Ma et al. 2010a).
They further investigated whether residue compensation was a necessary step for FH and declared that it was not indispensable if the FH algorithm did not incorporate dimension reduction methods such as PCA, or LPP which incur the loss of non-feature information (Ma et al. 2010b).
Li et al. (2009) claimed that the assumption adopted by many learning-based super-resolution methods that the low-resolution representation manifold and the corresponding high-resolution representation manifold share similar local geometry might not hold due to the non-isometric one-to-multiple mappings from low-resolution image patches to high-resolution image patches. They proposed a manifold alignment method for FH that projected the two manifolds to a common hidden manifold.
In this approach (Liu et al. 2001, 2007a), principal component analysis is first applied to obtain an initial global face image and subsequently an MAP-MRF is exploited to calculate the local face image.
Liu et al. (2007b) applied a two-step procedure to photo synthesis from an input sketch.
Liu et al. (2005a) (LLE-based) is used to generate an initial estimate. Then, by exploiting the proposed tensor model whose modes consisted of people identity, patch position, patch style (sketch or photo) and patch features, the high frequency residual error is inferred under the Bayesian MAP framework on the assumption that a sketch-photo patch pair shares the same tensor representation parameter.
By adding these two parts, a photo with much more detailed information could be synthesized from the input sketch.
Zhang and Cham (2008, 2011)proposed a FSR approach in the DCT domain under the MAP framework.
Unlike many LLE-based methods that assumed the low-resolution patch and high-resolution patch had the same reconstruction weights or coefficients,Park and Savvides (2007) proposed a LPP-based FSR, which inferred the LPP projection coefficients of each high-resolution patch via Bayesian MAP criterion from an input low-resolution image patch.
Kumar and Aravind (2008b) proposed a two-step method using orthogonal locality preserving projections (OLPP) (Cai et al. 2006) and kernel ridge regression (KRR).
Gunturk et al. (2003) proposed an eigenface-domain super-resolution method especially for face recognition
An image is decomposed into two parts: the low and middle frequency information part, and the high frequency information part, which results in the MAP objective function being solved by a two-step sequential solution. In the first step, the low and middle frequency information is evaluated by solving a least square problem. The high frequency information is then compensated by exploiting a non-parametric patch learning process in the second step. Combining these two parts, the target high-resolution image with some expression is computed.