NEIGHBOR EMBEDDING BASED SINGLE-IMAGE SUPER-RESOLUTION USING SEMI-NONNEGATIVE MATRIX FACTORIZATION
01 January 2012
input patch is compared to the stored LR patches and, once the nearest patch among these is found, the corresponding HR patch is finally taken as the output. A variation to this procedure is presented in [3] and in some other SR methods based on sparse representations (e.g. [4, 5]): instead of selecting from the dictionary only one patch, several patches are taken into account and contribute simultaneously to the generation of a single HR output patch. In particular, in [3] the authors propose a single-image SR algorithm, based on the concept of neighbor embedding and originally inspired by a method for data dimensionality reduction called Locally Linear Embedding (LLE) [6]. The basic assumption is that a patch in the LR target image and the corresponding HR unknown patch share similar neighborhood structures: as a consequence of that, once the LR patch is expressed as the linear combination of a certain number of its neighbors taken from the dictionary, the output patch can be reconstructed by using the HR patches in the dictionary corresponding to the neighbors selected, and combining them in the same way. This algorithm is shown to be suitable for the SR problem, but its performance is sensitive to the number of neighbors chosen, that appears as a parameter difficult to properly set. We propose a new neighbor embedding method based on Semi-nonnegative Matrix Factorization (SNMF) [7]. In LLE the weights are constrained to sum up to one, but no constraint is specified for their sign.
