Assessment of distorted MR images is a crucial process to evaluating various imaging techniques such as de-noising algorithms, reconstruction schemes for under-sampled data, and motion correction, etc. In optics, it has also been important to conduct image quality assessment (IQA)^{1, 2} in order to predict the quality of photographs taken from camera. When reference images are provided against subject images, which is the case of Full-Reference (FR), there are many objective evaluation methods like MSE, PSNR, SSIM², etc. These methods have been used for the assessment of MR images or techniques in previous studies^{3, 4}. However, it is impossible to use FR methods when there are only subject images without reference images, which is the case of No-Reference (NR). Therefore, NR IQA⁵ techniques have been recently investigated in optical photographs, which use big photo data that were previously taken from numerous pictures. Our purpose in this study is to develop and evaluate a new IQA methodology for NR-MRI such as in-vivo acquisitions directly from the scanners. The effectiveness of the proposed method is demonstrated for various kinds of image artifacts.

NR IQA makes it possible to obtain objective rating of distorted images. One of this methods uses opinion aware, which is associated with human evaluation and subjective opinion score. Another uses distortion aware using prediction of distortion or foreknowing the types of distortion such as gaussian noise or ghosting artifact. However, the technique proposed in this abstract is designed for evaluation without any above two cases ⁶. It evaluates distorted MR images using comparison with a numerical analyzer from pre-acquired MRIs (big data). The numerical analyzers were constructed using NIQE⁶ (Natural Image Quality Evaluator) technique. NIQE uses spatial NSS (Natural Scene statics) model which have high information of data and this is vital to explanation of images⁷.

$$Nss\left(x,y\right)=\frac{I\left(x,y\right)-m\left(x,y\right)}{\sigma\left(x,y\right)+1}...(equation1) $$

$$m\left(x,y\right)=\sum_{k=-K}^K\sum_{l=-L}^Lw\left(k,l\right)I\left(x+k,y+l\right)...(equation2) $$

$$\sigma\left(x,y\right)=\sqrt{\sum_{k=-K}^K\sum_{l=-L}^Lw\left(k,l\right)\left\{I\left(x+k,y+l\right)-m\left(x,y\right)\right\}^{2}}...(equation3)$$

$$$x\in\left\{1,2,3,...,M\right\}, y\in\left\{1,2,3,...,N\right\}$$$, image size is M by N, $$$Nss$$$ is NSS model, $$$I$$$ is images and $$$m$$$, meaning local mean function, is the convolution between image and gaussian weighting coefficient $$$w$$$ ($$$\sigma$$$ is the local deviation). $$$Nss$$$ conveys low-order statistics that are important factors for understanding images. Next, distorted images and analyzer are partitioned to several patches whose parts contain important structures excepting background and low information. Selected patches can be sorted by thresholding to local contrast. Finally, They are fitted to Multivariate Gaussian model (MVG) that effectively captures NSS features⁷.

$$f_{x}\left(x_{1},x_{2},...,x_{n}\right)=\frac{1}{2\pi^{k/2}|\Sigma|^{1/2}}exp{\left(-\frac{1}{2}\left(x-v\right)^T\Sigma^{-1}\left(x-v\right)\right)}...(equation4)$$

$$Q\left(v_1,v_2,\Sigma_1,\Sigma_2\right)=\sqrt{(v_1-v_2)^T(\frac{\Sigma_1-\Sigma_2}{2})^{-1}(v_1-v_2)}...(equation5)$$

NSS features of all patches, $$$x_{1},x_{2},...,x_{n}$$$ (n is # of patches) are fitted with MVG model (equation 4). By fitting process, mean matrix,$$$v$$$ , and covariance matrix,$$$\Sigma$$$, which are MVG parameters acquired from each patches. Assessment is obtained from equation 5, which is comparison between MVG model of distorted images and one of MR big data. The lower assessment value has better quality in NIQE. For numerical analyzer, this study chooses 113 MR images that consist of various T1-weighted and T2-weighted images. All of images (axial brain data) have high SNR and full sampling data from MP-RAGE sequence with 4 times acquisitions and averaging. Matrix size is the 256x256 and all images have different appearance each other. Next, evaluations are applied to distorted images that contain various white Gaussian noises, under-sampling artifacts and blur effect. In-Evaluated images were obtained from in-vivo T2-w (TR=3200ms, TE=109ms), T1-w (TR=250ms, TE=2.5ms), and PD-w (TR=3200ms, TE=11ms). Distorted images were generated with various distortions. To evaluate our proposed method, quantitative comparison were conducted between our proposed NR technique and conventional FR-based MSE method

Figure 2-4 show correlations between MSE (FR) and NIQE (NR). In figure 2, increasingly strong white Gaussian noise is added to MR images (10 cases). In figure 3, increasingly low-band low pass filter for blur effect is applied to MR images. In figure 4, under-sampling scheme in k-space data with reduction factor (R=1~10) is applied to the same images. White Gaussian noise and under-sampling artifact show strong correlations between MSE and NIQE. In case of blur effect, it shows weaker correlation than the others, but it still has a good correlation, showing the effectiveness of our method.This study demonstrated the feasibility of the proposed no-reference numerical analyzer for image quality assessment for MRI. White Gaussian noise, blur effects and under-sampling artifacts which are common in data acquisitions and reconstruction techniques were successfully evaluated without reference data. This technique can be applied to other types of distortions as well. Along with the big MR data still being accumulated, this technique bears high potential for various MR applications and assessments.