Synopsis

This paper proposes a new image quality assessment (IQA) for no-reference MRI, Quality Evaluation using Multi-DIrectional filters for MRI (QEMDIM), that is obtained from difference of statistical features between test images and numerous pre-scanned images in Mean Subtracted Contrast Normalization (MSCN) coefficient and Multi-Directional Filtered Coefficients (MDFC). the proposed method is capable of detecting various types of artifact and can be applied to clinical applications as well as being used to evaluate the performance of MRI hardware and software

Introduction

Methods

MR image statistics represent that the energy spectrum of MSCN coefficients have the form of a generalized Gaussian distribution (GGD).⁷ $$f(x;\alpha,\beta)=\frac{\alpha}{2\beta\Gamma(1/\alpha)}exp\left(-\left(\frac{\mid x\mid}{\beta}\right)^\alpha\right)$$ $$$\alpha$$$ and $$$\beta$$$ are the shape parameters of the GGD function. Each energy spectra of undistorted and distorted image have a different shape parameter. For example, the spectrum of Gaussian noise is wider than that of undistorted image. These differences can be obtained by fitting the spectrum to GGD function. We define the shape parameters as the quality-aware features. The relationship between these parameters is $$\beta=\sigma\sqrt{\frac{\Gamma(1/\alpha)}{\Gamma(3/\alpha)}}$$ Here, $$$\sigma$$$ is the standard deviation and $$$\Gamma(x)$$$ is the Gamma function $$\Gamma(x)=\int_{0}^{\infty}t^{x-1}e^{-t}dt,\space\space\space x>0$$ MSCN coefficients, the truly spatial domain, are more perception-friendly domain and have low computation time than co-ordinate domain such as wavelet and DC. The MSCN coefficient is $$\hat{I}(x,y)=\frac{I(x,y)-\mu(x,y)}{\sigma(x,y)+C}$$ where $$$x\in\left\{1,2,3,...,N\right\}$$$ and $$$y\in\left\{1,2,3,...,M\right\}$$$ are spatial indices and $$$I(x, y)$$$ is magnitude of the image. The terms $$$\mu$$$ and $$$\sigma$$$ are mean and standard deviation of $$$I(x, y)$$$. The quality-aware features are obtained in MSCN coefficients using generalized Gaussian ration (GGR) function⁷, which is made up of the shape parameters. The MSCN coefficients can detect non-directional distortions because of their 2D-circle subtraction. However, the common distortions in MRI like motion artifact have directional structure. Therefore, we propose multi-directional filtered coefficients (MDFC) for evaluation of directional distortions. MDFCs are calculated from various steps. Firstly, we make multi-directional filters, $$$W_{G}$$$ , a 2D Gaussian low-pass filter. Next multi-directional gradient vectors can be defined as $$HD_{1}=\begin{bmatrix}-1&1\end{bmatrix},HD_{2}=\begin{bmatrix}-1&1\end{bmatrix}^T,HD_{3}=\begin{bmatrix}-1&0\\0&1\end{bmatrix},HD_{4}=\begin{bmatrix}0&-1\\1&0\end{bmatrix}$$ $$$HD_{1}$$$, $$$HD_{2}$$$, $$$HD_{3}$$$, $$$HD_{4}$$$ are vertical, horizontal, and two diagonal gradient filters, respectively. Multi-directional filters are generated by convolution between $$$HD_{k}$$$ and $$$W_{G}$$$ $$DF_{k}=W_{k}*HD_{k}$$ From above equation, multi-directional filters $$$DF_{k}$$$ are generated and convoluted with the MSCN coefficients Finally, MDFC coefficients are calculated from $$FC_{k}=M(x,y)*DF_{k}(n,m)$$ Since directional coefficients have GGD regularity⁹, the quality-aware features can be extracted from MDFCs. A total of 10 parameters, 2 shape parameters form the MSCN coefficients and 8 shape parameters from four regions of MDFCs are obtained from one patched image.

The quality evaluator is calculated from $$$D=\sqrt{(P_{r}-P_{e})^T(P_{r}-P_{e})}$$$ where $$$P_{r}$$$ and $$$P_{e}$$$ are the quality-aware features of the training databases and distorted images, respectively. In our experiments, database was provided T2-FLAIR brain images from ADNI⁸. Figure 1 shows entire processes of QEMDIM.

Results

Acknowledgements

References

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