Single image super-resolution via blind blurring estimation and anchored space mapping

10.1007/s41095-016-0043-7.F1 Fig. 1Description of cross-scale patch redundancy. For each small patch ${𝒑}_i$ in $𝒀$ , finding its NNs ${𝒒}_{ij}^s$ in ${𝒀}^s$ which corresponds to a large patch ${𝒒}_{ij}$ in $𝒀$ , ${𝒒}_{ij}^s$ and ${𝒒}_{ij}$ constitute a patch pair, and all patch pairs of NNs construct a set of linear equations which is solved using weighted least squares to obtain an updated kernel.

10.1007/s41095-016-0043-7.F2 Fig. 2Blurring effect on non-smooth and smooth areas. Black boxes indicate structured areas, and red boxes indicate smooth areas. (a) Clean patches. It can be clearly seen that the structure of non-smooth patch is distinct. (b) Blurred patches corresponding to (a). The detail of non-smooth patch is obviously blurry.

10.1007/s41095-016-0043-7.F3 Fig. 3Feature extraction strategy. $𝒆(\cdot )$ represents the enhanced interpolation operation. The down-sampled version ${𝒀}^s$ is obtained by convolving with estimated kernel $\widehat{𝒌}$ and down-sampling with $s$ . LR feature set consists of normalized gradient feature patch extracted from ${𝒀}^{\prime }$ , HR feature set is made up with the raw patches extracted from BPR image $𝒀-{𝒀}^{\prime }$ .

10.1007/s41095-016-0043-7.F4 Fig. 4Comparisons between statistical characteristics and threshold effect on estimated kernels. The testing images are "baboon" from Set14 and "high-street" from Set2, and the blur kernels are a Gaussian with $hsize=5$ and $sigma=1.0$ (9 $\times$ 9) and a motion kernel with $length=5,$ $theta=135$ (11 $\times$ 11) respectively. We only display estimated kernels when threshold on $|$ grad $|$ $⩽$ 50.

10.1007/s41095-016-0043-7.F5 Fig. 5Visual comparisons of SR recovery with low-quality "butterfly" image from Set5 ( $\times 2$ ). The ground-truth kernel is a 9 $\times$ 9 Gaussian kernel with $hsize=5$ and $sigma=1.25$ , and threshold on $|$ grad $|$ is 18.

10.1007/s41095-016-0043-7.F6 Fig. 6Visual comparisons of SR recovery with low-quality "high-street" image from Set2 ( $\times 3$ ). The ground-truth kernel is a 13 $\times$ 13 motion kernel with $len=5$ and $theta=45$ , and threshold on $|$ grad $|$ is 24.

10.1007/s41095-016-0043-7.F7 Fig. 7Visual comparisons of SR recovery with low-quality "zebra" image from Set14 ( $\times 3$ ). The ground-truth kernel is a 13 $\times$ 13 Gaussian kernel with $hsize=5$ and $theta=1.25$ , and threshold on $|$ grad $|$ is 16.

10.1007/s41095-016-0043-7.F8 Fig. 8Visual comparisons of SR recovery with low-quality "tower" image from B100 ( $\times 2$ ). The ground-truth kernel is a 11 $\times$ 11 motion kernel with $len=5$ and $tehta=45$ , and threshold on $|$ grad $|$ is 17.

10.1007/s41095-016-0043-7.F9 Fig. 9Visual comparisons of SR recovery with real low-quality image "fence" captured with slight joggle ( $\times 2$ ). Threshold on $|$ grad $|$ is 21.

10.1007/s41095-016-0043-7.F10 Fig. 10Visual comparisons of SR recovery with real low-quality image "building" captured with slight motion ( $\times 2$ ). Threshold on $|$ grad $|$ is 26.