Learning Hierarchical Decision Trees for Single-Image Super-Resolution

Sparse representation has been extensively studied for image super-resolution (SR), and it achieved great improvement. Deep-learning-based SR methods have also emerged in the literature to pursue better SR results. In this paper, we propose to use a set of decision tree strategies for fast and high-quality image SR. Our proposed SR using decision tree (SRDT) method takes the divide-and-conquer strategy, which performs a few simple binary tests to classify an input low-resolution (LR) patch into one of the leaf nodes and directly multiplies this LR patch with the regression model at that leaf node for regression. Both the classification process and the regression process take an extremely small amount of computation. To further boost the SR results, we introduce a SR using hierarchical decision trees (SRHDT) method, which cascades multiple layers of decision trees for SR and progressively refines the estimated high-resolution image. Inspired by the random forests approach, which combines regression models from an ensemble of decision trees, we propose to fuse regression models from relevant leaf nodes within the same decision tree to form a more robust approach. The SRHDT method with fused regression model (SRHDT_f) improves further the SRHDT method by 0.1-dB in PNSR. Our experimental results show that our initial approach, the SRDT method, achieves SR results comparable to those of the sparse-representation-based method and the deep-learning-based method, but our method is much faster. Furthermore, our enhanced version, the SRHDT_f method, achieves more than 0.3-dB higher PSNR than that of the A+ method, which is the state-of-the-art method in SR.

I. Introduction

Single-image super-resolution (SR) aims to increase the resolution of a single-input low-resolution (LR) image by upsampling, deblurring, and denoising, while the resultant high-resolution (HR) image should preserve the characteristics of natural image, such as sharp edges and rich texture. The LR image X in the SR problem is assumed to be a blurred and downsampled version of the original HR image Y

$$\begin{equation} {\mathbf{X}}={\mathbf{DHY}}+{\mathbf{n}} \end{equation}$$ where D is the downsampling operator, H is the blur operator, and n is the additive noise.