# No-Reference Blurred Image Quality Assessment by Structural Similarity Index
## 1 Introduction  
Advances in digital techniques enable people to capture, store and send a large amount of digital images easily, which sharply accelerates the rate of information transfer. Images captured by cameras in the real world are usually subject to distortions during acquisition, compression, transmission, processing, and reproduction. The information that an image conveys is related to image quality, thus image quality is very significant for image acquisition and processing systems. If the quality of an image is bad, its processing result is usually bad as well. Therefore, image acquisition and processing systems in real applications need image quality assessment (IQA) to objectively and automatically identify and quantify these image quality degradations. In recent decades, many IQA methods have been proposed to solve this problem. IQA methods can be classified as full-reference (FR), no-reference (NR) and reduced-reference (RR) methods. FR methods, such as the mean squared error (MSE), the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM) [1], require the original undistorted images as the references. In addition, RR methods need prior information about the original images, but either the original undistorted images or their prior information are rarely obtained in practice. NR methods can assess the quality of the distorted images only using themselves, thus are more suitable for actual applications. In this paper, we confine our work to NR methods and focus on the degradation of blur.  
The popular FR metric SSIM [1] takes advantage of mathematical convenience and matching to known characteristics of the human visual system (HVS) but suffers from a lack of pristine referenceimages. Recent general NR models, such as [2; 3; 4], perform well when adapting with HVS, but lose computation convenience when training with distorted images in advance. In this paper, we propose an NR IQA method for blurred images. Our proposed metric, called no-reference structural similarity (NSSIM), is based on re-blur theory and SSIM, and can be regarded as an improvement of SSIM from FR to NR. The first part is the _re-blur_ process, i.e., blurring the distorted images by a Gaussian low-pass filter. The second is to quantify the blurriness of the image by grayscale distribution. Finally we combine luminance, contrast, structure and blurriness to a quality score. Our NSSIM can be easily computed using the input image and its re-blurred image, and no previous training is needed. Experimental results from four popular datasets validate the better performance of NSSIM than the compared FR and NR methods. In addition, we apply NSSIM to evaluate the performance of the blurred image restoration. The results demonstrate that NSSIM performs as well as the state-of-the-art NR IQA metrics and can get better image quality evaluation than the existing FR IQA metrics PSNR and SSIM. The contribution of the paper is two-fold. One is that we propose a novel definition of image blurriness based on the grayscale distribution of the image, and verify its effectiveness of blurriness measurement and fitness with the subjective quality sense of a human. The other is that we extend the famous FR IQA metric SSIM to a no-reference manner, achieving state-of-the-art IQA performance without previous training.  
The rest of this paper is organized as follows. In Section 2, we review previous works in IQA. In Section 3, we describe the blurriness definition and computation, and procedure of our model. In Section 4, we evaluate the performance of the proposed approach by comparing it with the state of the art and applying for blurred image restoration. Section 5 concludes the paper.