Adaptive shock filter for image super-resolution and enhancement

Highlights

• Adaptive shock filter is used to reduce distortion artifacts of upsampled images.

• Both edge-stopping function term and forward diffusion process term are proposed.

• The weight of shock filter relies on the gradients of the interpolated image.

Abstract

In view of that image interpolation methods generally tend to produce considerable edge halos, blurring and aliasing artifacts for image super-resolution. A novel image enhancement algorithm based on adaptive shock filter for image super-resolution is proposed to solve this problem. The weight of shock filter can be adjusted adaptively according to the gradients of the interpolated high-resolution image. Thus the diffusion of image edges is suppressed and the artifacts are removed by the forward diffusion. Compared with the traditional shock filter, the proposed algorithm eliminates edge halos and jagged artifacts, whereas the fine image structures are reserved effectively. Theoretical analysis and experimental results demonstrate that the proposed algorithm can achieve better results than the state-of-the-art methods both subjectively and objectively in most cases.

Introduction

The goal of image super-resolution is to construct a high resolution (HR) image from a single frame or multiple low resolution (LR) images. Recently, it has become the focus of the study in many applications, such as remote sensing, military, medical imaging, public security and 3D image [1]. After a brief review on image super-resolution (SR), the SR methods are mainly divided into four categories [2]. The interpolation methods produce the HR images by using the basis function of smooth curve or curved surface. The reconstruction-based methods construct the HR image by minimizing the regularized cost function with image priors or constraints, which are usually involved with the motion estimation and registration of multi-frame images [3]. The example-based methods exploit the relationship between the HR and LR image patches for super-resolution reconstruction, or magnify the LR images by the interpolation method and then enhance the interpolated results for image super-resolution. This paper focuses on the study of single frame super-resolution based on image interpolation and enhancement.

The interpolation methods can be further divided into two categories: linear methods and nonlinear methods. The typical linear methods include nearest neighbor interpolation, the bilinear interpolation, and double three interpolation methods. These interpolation methods have high efficiency, but they tend to cause jaggy effect or loss of texture details and results in blurred images. Nonlinear interpolation methods can overcome the above shortcomings to a certain extent, e.g., the edge directing interpolation [4], the statistical interpolation [5], and the outline template interpolation [6]. However, these interpolation methods based on the local information of LR images cause the diffusion of edges and lead to blurred image and the interpolated noise.

In recent years, the partial differential equations(PDE) have been widely used in image restoration and image enhancement [7], [8], [9], [10]. The initialization of the PDE-based image super-resolution is obtained from the LR image by the interpolation methods. After solving the PDE equation, the HR image is obtained by image denoising and enhancement. Osher and Rudin [11] proposed a shock filtering model for image sharpening and enhancement. But this method also amplifies the noise. The module has good results for clean images. But it cannot remove some kind of noise, e.g., “salt and pepper” noise. Then if we have a noisy signal, it produces a lot of spurious shocks due to the influence of noise. Alvarez and Mazorra [12] introduced the Gaussian kernel function and the forward diffusion for noise reduction of image enhancement. However, it also produces fake edges, jaggy artifacts and blocking effects. The enhanced images have discontinuity edges and some isolated blocking effects. Kornprobst and Deriche [13] tuned the thresholding value to adjust the weight of shock filtering and forward diffusion. But it also causes the blurring and jaggy artifacts due to the discontinuities of the weight. Gilboa et al. [14] proposed a complex-domain shock filtering and diffusion process for image enhancement and denoising, where the imaginary part was served as an edge detector. This method can avoid the blurring artifacts, but it also causes loss of abundant details. Fu et al. [15], [16] proposed a region-based shock filtering for adaptive image enhancement. The artificial effects are decreased by use of continuous weight. But the coefficient of weight is determined by the second order directional derivative of images. The jaggy artifacts appear at certain image edges where the gradient changes fast. Subsequently, Bettahar and Stambouli [17], [18] proposed an image denoising and sharpening scheme based on curvature diffusion and shock filter. But its drawback is too complex with heavy computation.

It is found that the super-resolution methods based on interpolation have artificial defects, such as diffusion of edges, blocking effect, sawtooth effect and the interpolated noise. To solve these problems, a novel image enhancement algorithm based on adaptive shock filtering (ASF) model is proposed for image super-resolution. The weight of each shock filtering is determined by image gradients. By use of hyperbolic tangent function, the proposed algorithm can reduce the diffusion of image edges and the noise effectively. Moreover, our proposed algorithm has less sawtooth effects and blocking artifacts and can recover more fine structures than the traditional shock filter.