Introduction

The Quality Evaluation using Multi-Directional Filters for MRI (QEMDIM) has been proposed as a no-reference image quality assessment (IQA) algorithm.¹ The algorithm (Fig. 1) requires a pair of input, including an image to be assessed (assessed image) and a set of reference images (reference set). The quality of the reference set may affect the quality scores of the QEMDIM algorithm. This study aimed to investigate the effect of the quality of the reference set on QEMDIM scores. Further, we proposed a modified algorithm to compensate for such a drawback of the QEMDIM algorithm.

Theory

The QEMDIM score (S_Q) is calculated based on the Euclidean distance between two feature vectors each with 20 elements:$$S_Q=\|\boldsymbol{f_r-f_a}\|\qquad(1)$$where $$$\boldsymbol{f_r}$$$ and $$$\boldsymbol{f_a}$$$ are the column feature vectors of the reference set and assessed image, respectively (Fig. 1). The QEMDIM score is a non-negative number with high values indicating large differences in quality between the assessed image and the reference set.
Our proposed algorithm is the same as QEMDIM (Fig. 1), except for the calculation of the quality score. The score in our algorithm (modified score, S_mod) can be obtained using the following equation:$$S_{mod}=\frac{\boldsymbol{f_r}\cdot(\boldsymbol{f_r-f_a})}{\|\boldsymbol{f_r}\|}\qquad(2)$$where “$$$\cdot$$$” is the inner product operator. A highly positive (low negative) value of the modified score is expected to indicate that the assessed image has a higher or lower quality than the reference set and a value of zero indicates that the assessed image has the same quality as the reference set.

Methods

Five T₁-weighted (T₁W) and five T₂-weighted (T₂W) spin-echo scan data of brain axial planes were acquired for healthy volunteers using a 3.0-T MR scanner (SIGNA Architect, GE Healthcare) and a 48-channel head coil. The scan parameters that differed between T₁W and T₂W imaging were the repetition time (TR), echo time (TE), and number of excitations (NEX): TR[ms]/TE[ms]/NEX = 545/12/8 for T₁W imaging, and 3500/80/2 for T₂W imaging. Other parameters were as follows: Cartesian trajectory, field-of-view = 22 cm, slice thickness = 2 mm, spacing = 2 mm, number of slices = 12, and acquisition matrix = 256×256. Each of the acquired scan data was used to reconstruct 16 T₁W and 8 T₂W image series with various image qualities (four levels of NEX × 4 levels of the number of phase-encoding steps (Ny) for T₁W images and 2 NEX’s × 4 Ny’s for T₂W images). A total of 960 T₁W and 480 T₂W images were obtained (Fig. 2).
Sixteen T₁W and eight T₂W images, of different qualities though showing the same contents (Fig. 2), were used as samples in our observation experiment. The observation consisted of the T₁W and T₂W sessions, and ten radiological technologists participated in each session. Two images were simultaneously displayed on a monitor, and the observers were asked to evaluate the relative and comprehensive image quality on a 3-point scale (left one is better, they are similar, or right one is better). The 3-point-scale evaluations were repeated for 240 image pairs ($$${}_{16}\mathrm{P}_2$$$) in the T₁W session and 56 image pairs ($$${}_{8}\mathrm{P}_2$$$) in the T₂W session. The paired comparison (Schéffe method ²) was used to calculate the average degree of preference (subjective score, S_subj) for each image. S_subj can range between $$$[-1, 1]$$$ and indicates a high value when the image has high quality.
We prepared 16 T₁W and 8 T₂W reference sets, each consisting of all the reconstructed images with consistent quality (NEX and Ny) (Fig. 2). S_Q and S_mod were computed for all T₁W or T₂W pairs of a reconstructed image and a reference set.
The reconstructed images were divided into the 60 image-content subsets, each consisting of 16 T₁W and 8 T₂W images with different qualities and the same contents (Fig. 2). Under the assumption that the variation in the quality (S_subj) among images belonging to each image-content subset is the same, the Pearson linear correlation coefficients between S_subjs and S_Qs (CC_Q,subj) and between S_subjs and S_mods (CC_mod,subj) were calculated for each image-content subset. The Kruskal-Wallis test was used to analyze the effect of the quality of the reference set on CC_Q,subj and CC_mod,subj.

Results

The distribution of CC_Q,subj varied significantly with the quality of the reference set (Fig. 3b and d). There was no significant variation in the CC_mod,subj distributions (Fig. 3a and c). The CC_mod,subj showed consistently high positive values (mean ± SD: 0.93 ± 0.023 for T₁W images; and 0.97 ± 0.016 for T₂W images) irrespective of the quality of reference set.

Discussion and Conclusion

Subjective image quality is the gold standard in clinical practice. S_mod showed a high correlation with S_subj, irrespective of the quality of the reference set, while S_Q did not. Therefore, the QEMDIM algorithm might not be able to accurately evaluate the MR image as it may be influenced by the quality of the reference set. Our modified IQA algorithm could be more useful and robust in clinical practice than the QEMDIM algorithm and has the potential to be an alternative to subjective IQA.

References

1. Jang J, Bang K, Jang H, et al. Quality Evaluation of No-Reference MR Images Using Multidirectional Filters and Image Statistics. Magn Reson Med. 2018;80(3):914–924.

2. Nagasawa S. Improvement of the Schéffe’s method for paired comparisons. Kansei Eng Int. 2002;3(3):47–56.