In this project, medical X-Ray imaging methods using MATLAB tools are studied. In order to design the model of the X-Ray imaging as software, the X-Ray imaging project is divided into two parts, namely the forward problem and the inverse problem.
The first part is the forward problem which takes the image to be projected as an input. According to the number of sampling points in each projection, projection angles, and the degrees of rotation of the image, which the user specifies, the vectors of the projections, in other words, line integrals, for a 2-D object with known attenuation coefficients are calculated.
In the second part, the inverse problem, the algorithm reconstructs the 2-D image, in other words, attenuation coefficient distribution, using the projections calculated in the first part of the project. Since a blurring effect exists in the reconstructed images, various filters, namely Hann and Blackman, are applied to suppress this blurring effect. After reconstructing the image, the filters’ performance is calculated using different metrics, such as Mean-Squared Error, PSNR, and SSIM scores. Finally, the performance of the filters is discussed.
X-ray imaging has been a crucial instrument in the medical industry for more than a century. Since Wilhelm Röntgen discovered it in 1895, it has been used extensively to diagnose and treat various medical diseases.
In X-ray imaging, the algorithms projection and filtered back projection are often employed. A two-dimensional representation of a three-dimensional object, such as the human body, is produced using projection. A sequence of X-ray beams is sent through the body and onto a detector on the opposite side to accomplish the task. The detector measures the strength of the X-ray photons that enter the body and uses this information to produce a picture of the interior organs.
On the other hand, filtered back projection is a method that uses the projection technique's projection data to rebuild a picture. It reconstructs the picture by first applying a mathematical filter on the projection data and then utilizing the filtered data. The end product is a comprehensive, two-dimensional illustration of the interior anatomy of the body. Both the projection and the filtered back projection algorithms are crucial components of medical X-ray imaging because they let medical professionals build precise pictures of the inside of the body and identify and cure a wide range of illnesses.
In this study, an input image with known attenuation coefficients is projected according to the inputs specified by the user. Users can decide the input image to be projected, the number of sampling points, projection angles, and rotation angle to rotate the image. These input parameters are used to calculate the projection of the input image, and projection data is created. Then, this data is used to reconstruct the original image using a back projection algorithm. While reconstructing the image, different filters are applied to obtain a more accurate result and cancel the blurring effect. Finally, the Mean-Squared Error, PSNR, and SSIM scores are calculated for both unfiltered and filtered reconstructed images, and their performances are compared. Moreover, to increase the project's usability and to have a user-friendly environment, a graphical user interface (GUI) is designed via the App Designer tool of MATLAB.
In the forward projection algorithm, the projections for a 2-D object are calculated. These projections are obtained by making respective drawings by the angle of θ through t axis which can be achieved by taking line integrals. The formula for the line integral can be expressed as:
The path, L, of the integration is described by this expression:
By taking the line integral, the conversion between (θ,t) and (x,y) parameters are completed. So, the projection function is ready to be implemented in the Cartesian coordinated by this formula:
The projection angle, θ, is the angle between the x-axis and the line normal to the X-Ray path. To accomplish the calculation of the line integrals, the multiplication of each beam within each pixel and the attenuation coefficient of this pixel is calculated, and the along this beam, the result of the multiplication is added and stored.
In the Back Projection algorithm, the projection data is already calculated by the Forward Projection algorithm. That’s why this data is used in order to reconstruct the original image according to this formula:
As it was calculated in the Forward Projection algorithm, the data for all beams and angle of projections are multiplied and the distance that is taken is multiplied with this result. For each pixel this multiplication results are stored to reconstruct the original image. But there exists a problem while reconstructing the original image. Since the impulse responses of the projection and back projections are studied, the reconstructed image is multiplied by the (1/ρ) coefficient, which is called as blurring effect. In order to cancel this blurring effect, high pass filters are applied.
In this project, Ram Lak, Hann and Blackman filters are applied and their corresponding performances are compared.
To test the algorithms, “SheppLogan” image is used.
In the first test, these parameters are used:
- Number of Beams: 100
- Size Of Step: 1
- Rotation Angle: 0
Input Image
Projection Data
Reconstructed Images
Mean-Squared Error, SSIM and PSNR Scores for different filters
| Filter Name | Triangular | Hann | Blackman |
|---|---|---|---|
| Mean-Squared Error | 0.0040 | 0.0156 | 0.0208 |
| SSIM | 0.5834 | 0.4708 | 0.4286 |
| PSNR | 23.9909 | 18.0701 | 16.8155 |
In the second test, these parameters are used:
- Number of Beams: 1000
- Size Of Step: 1.8
- Rotation Angle: 0
Input Image
Projection Data
Reconstructed Images
Mean-Squared Error, SSIM and PSNR Scores for different filters
| Filter Name | Triangular | Hann | Blackman |
|---|---|---|---|
| Mean-Squared Error | 0.0024 | 0.0028 | 0.0029 |
| SSIM | 0.6064 | 0.6068 | 0.6058 |
| PSNR | 26.1186 | 25.5609 | 25.3326 |