# Image Quality Assessment to Emulate Experts' Perception in Lumbar MRI Using Machine Learning
## 2 Methods and Materials
### Machine Learning  
In the process for classifying exams into \"good\" or \"deficient\" it was decided to apply five techniques of machine learning that are well known and widely used in the state of the art. Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) are classifiers with a linear or quadratic decision limit, respectively, generated from adjusting the conditional densities of the data classes using the Bayes rule [29]. Another of the most used algorithms is the Support Vector Machine (SVM) technique. The SVM is a supervised learning classifier utilized for the prediction of class labels. It transforms features into a higher dimension space, where it implements the optimal hyperplane that describes the classes. The hyperplane work is based on the maximum margin between \begin{table}
\begin{tabular}{l l l} \hline \hline
**Feature** & **Definition** & **Apply to** \\ \hline Slice thickness & From DICOM metadata & Whole image \\ Pixel dimension & From DICOM metadata & Whole image \\ Brightness & Average intensity & Whole image \\ Image CNR & \(max(\mathbf{I})-min(\mathbf{I})\) & Whole image \\ Relative CNR & \(\frac{ImageCNR}{Brightness}\) & Whole image \\ Signal to Noise Ratio \(SNR_{i}\) & \(S_{i}\big{[}\frac{\sigma}{0.685}\big{]}^{-1}\) & \\ Contrast to Noise Ratio \(CNR_{ij}\) & \((S_{i}-S_{j})\big{[}\frac{\sigma}{0.685}\big{]}^{-1}\) & \\ \hline \multirow{4}{*}{Uniformity \(U_{i}\)} & \(U_{i}=1-\frac{AAD_{i}}{S_{i}}\) where & \\  & \(AAD_{i}=\sum_{k=1}^{N_{pix}}\frac{S_{k}-S_{k}}{N_{pix}}\) & \\ \cline{1-1} Foreground Background Energy Ratio & \(\frac{E_{f}}{S_{k}}\) where \(E=\sum_{k=1}^{Npix}S_{u}^{2}\) within & \\ FBER & foreground and background resp. & \\ \cline{1-1} Wang Index & See [25] for details & \\ Image Sharpness & \(\frac{1}{N_{x}N_{y}}\sum_{n=1}^{N_{x}}\sum_{n=1}^{N_{y}}\big{|}\frac{\
abla S _{ox}}{S_{un}}\Big{|}^{2}S_{uv}\) & \\ \cline{1-1} Image Sharpness in fat & Same as Image Sharpness, but applied in ROI within fat & ROI within fat \\ Shannon Entropy & \(-\sum_{k=1}^{B}p_{k}log(p_{k})\) & Whole image \\ Entropy Power & \(SpectralFlatness*\frac{\sum_{k=1}^{N_{x}}\frac{\sum_{k=1}^{N_{y}}|S_{un}-\mathbf{I }|^{2}}{N_{x}N_{y}}}{N_{x}N_{y}}\) & Whole image \\ Spatial Flatness & \(\frac{\big{(}\mathbf{I}_{k=1}^{N_{x}N_{y}}|\mathbf{z}_{k}(k)|^{2}\big{)}^{ \frac{1}{N_{x}N_{y}}}}{\frac{1}{N_{x}N_{y}}\sum_{k=1}^{N_{x}N_{y}}\left|\mathbf{ r}_{k}(k)\right|^{2}}\) & Whole image \\ Spectral Flatness & \(\frac{\big{(}\mathbf{I}_{k=1}^{N_{x}N_{y}}|\mathbf{r}_{k}(0)|^{2}\big{)}^{ \frac{1}{N_{x}N_{y}}}}{\frac{1}{N_{x}N_{y}}\sum_{k=1}^{N_{x}N_{y}}\left|\mathbf{ r}_{k}(k)\right|^{2}}\) & Whole image \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of features extracted for the objective image quality evaluation. Variables are explained in the main text. itself and those nearest to it. The nearest set of points are called support vectors [30]. Another method is Logistic regression (LogReg), a statistical approach for predicting binary classes. The outcome or target variable is dichotomous in nature, and the model computes the probability of an event occurrence using a logit function [31]. Finally, the Multi layer perceptron (MLP) is a supplement of the feed forward neural network, and consists of three types of layers: the input layer (it receives the input signal to be processed), output layer (It performs the task) and hidden layer (the true computational engine of the MLP). Similar to a feed forward network, in an MLP the data flow in the forward direction from input to output layer and the neurons are trained with the back propagation learning algorithm. MLPs are designed to approximate any continuous function and can solve problems which are not linearly separable. The major use cases of MLP are pattern classification, recognition, prediction and approximation [32]. These five algorithms (LDA, QDA, SVM, LogReg and MLP) were implemented in python 3.6 using the ScikitLearn toolbox in version 0.16.1 [33].