Application of regularization methods to computed tomography images

In medical imaging, deblurring computed tomography (CT) images is very important. When CT images are blurred, important details can be obscured, and accurate diagnosis can be hindered. As CT images obtained using X-rays are reconstructed into slices, they can become blurred due to motion artifacts, hardware, and software problems. This blurring makes it difficult for radiologists to interpret the image. In this study, to remove the blurring of these images, the Fast Fourier Transform (FFT) was used to transform the CT images into the frequency domain. With this process, the image is transferred from the time domain to the frequency domain. In this way, the frequency components of the image were obtained. The General Tikhonov method is used to enhance CT images with noisy or missing data. This improves the quality of the restored image by incorporating prior information about the image (e.g., smoothness). When Laplace filtering was applied to the image, edges and sharp transitions in the image were emphasized. In this study, we propose a method that utilizes a larger size Laplace filter in the General Tikhonov method based on the Fast Fourier transform. The proposed method is compared with similar methods in the literature, and it is shown that the method produces effective results.