Single-Image Super-Resolution via Adaptive Joint Kernel Regression

Single image super-resolution (SR) methods can be broadly categorized into three classes: interpolation-based methods, reconstruction-based methods [7], and example-based methods [2, 3, 6]. The reconstruction-based methods often incorporate prior knowledge to regularize the ill-posed problem. For example, Zhang et al. [7] assembled the Steering Kernel Regression [5] (SKR)-based local prior and Nonlocal Means [1] (NLM)based nonlocal prior. The example-based methods strongly rely on the chosen dictionary for satisfactory results. This paper focuses on learning good image priors and robust dictionaries for SR reconstruction. Among the extensively studied natural image priors, we choose to exploit the local structural regularity prior and nonlocal self-similarity prior in a coherent framework. We propose in this paper an Adaptive Joint Kernel Regression (AJKR)based prior to simultaneously exploit both image statistics. Our approach differs from others in several ways: 1) we combine a set of NLM-generalized local kernel regressors, which are more consistent with our nonlocal collaborative framework; 2) the proposed regional redundancy measure introduces higher-order statistics at the region level for each regression group, making the overall framework more adaptive (see Fig. 1(a)); and 3) an adaptive PCA-based dictionary learning scheme is adopted to bridge the gap of dictionaries learned online and offline by mixing them, and more importantly such a scheme together with its induced sparsity prior can adapt to the AJKR process in response to the regional redundancy measure (see the block diagram in Fig. 1(b)). The imaging model for SR (assume Y ∈ Rm is low resolution (LR) image, X ∈ Rn is high resolution (HR) image) is usually expressed as