Learning local Gaussian process regression for image super-resolution

Single-Image Super-Resolution based on Steering Kernel and Gaussian Process Regression

Single-image super-resolution (SR) imaging is a fundamental problem in image processing; it is important in entertainment, video surveillance, remote sensing, medicine, and other fields. Gaussian process regression (GPR) is a kernel method whereby nonlinear mapping relationships in data can be learned. However, the traditional Gaussian kernel function used in GPR is isotropic and fails to capture complex image structures. Accordingly, the structure information of image patches, termed steering kernel coefficients (SKCs), is extracted by a steering kernel function. After patches with similar structure are clustered according to their SKCs, an anisotropic automatic-relevance-determination (ARD) kernel function is used to learn the model for each cluster. Aiming at learning a structure-sensitive GPR model, we integrate the SKCs and ARD to achieve improved performance for GPR-based SR. Experiments demonstrate that the proposed method can effectively capture the structural relevance of image patches and yield promising results.

Single Image Super-Resolution Using Gaussian Process Regression With Dictionary-Based Sampling and Student- ${t}$ Likelihood

Gaussian process regression (GPR) is an effective statistical learning method for modeling non-linear mapping from an observed space to an expected latent space. When applying it to example learning-based super-resolution (SR), two outstanding issues remain. One is its high computational complexity restricts SR application when a large data set is available for learning task. The other is that the commonly used Gaussian likelihood in GPR is incompatible with the true observation model for SR reconstruction. To alleviate the above two issues, we propose a GPR-based SR method by using dictionary-based sampling (DbS) and student-t likelihood. Considering that dictionary atoms effectively span the original training sample space, we adopt a DbS strategy by combining all the neighborhood samples of each atom into a compact representative training subset so as to reduce the computational complexity. Based on statistical tests, we statistically validate that student-t likelihood is more suitable to build the observation model for the SR problem. Extensive experimental results show that the proposed method outperforms other competitors and produces more pleasing details in texture regions.