# Image Super-Resolution Via Sparse Representation

##### Citations

6,639 citations

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5,902 citations

5,668 citations

### Cites methods from "Image Super-Resolution Via Sparse R..."

...They group super-resolution techniques into prediction-based methods (bilinear, bicubic, Lanczos, [24]), edgebased methods [25,26], statistical methods [27,28,29], patch-based methods [25,30,31,32,33,34,35,36], and sparse dictionary methods [37,38]....

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4,770 citations

### Cites methods from "Image Super-Resolution Via Sparse R..."

...This approach is proposed in the methods of [47, 8]....

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##### References

40,785 citations

### "Image Super-Resolution Via Sparse R..." refers background in this paper

...Rather than demanding that be perfectly reproduced by the sparse coefficients , we can penalize the difference between and the high-resolution image given by these coefficients, allowing solutions that are not perfectly sparse, but better satisfy the reconstruction constraints....

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18,609 citations

15,106 citations

### "Image Super-Resolution Via Sparse R..." refers background in this paper

...[11] adopts the philosophy of locally linear embedding (LLE) [12] from manifold learning, assuming similarity between the two manifolds in the high-resolution and the low-resolution patch spaces....

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11,500 citations

### "Image Super-Resolution Via Sparse R..." refers background in this paper

...To be precise, the solution is also approached in two steps: 1) global model: use reconstruction constraint to recover a medium high-resolution face image, but the solution is searched only in the face subspace; and 2) local model: use the local sparse model to recover the image details. a) Nonnegative Matrix Factorization (NMF): In face SR, the most frequently used subspace method for modeling the human face is principal component analysis (PCA), which chooses a low-dimensional subspace that captures as much of the variance as possible....

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...Nonnegati ve Matrix Factorization (NMF) [31] seeks a representation of t he given signals as an additive combination of local features....

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...Column 4 shows the intermediate results from the NMF global modeling and column 5 demonstrates the results after local sparse modeling....

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...NMF [29] seeks a representation of the given signals as an additive combination of local features....

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...To find such a part-based subspace, NMF is formulated as the following optimization problem: (12) where is the data matrix, is the basis matrix and is the coefficient matrix....

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9,604 citations