Browsing by Subject "Inverse problems"

The applied mathematical field of inverse problems studies how to recover unknown function from a set of possibly incomplete and noisy observations. One example of real-life inverse problem is image destriping, which is the process of removing stripes from images. The stripe noise is a very common phenomenon in various of fields such as satellite remote sensing or in dental x-ray imaging. In this thesis we study methods to remove the stripe noise from dental x-ray images. The stripes in the images are consequence of the geometry of our measurement and the sensor. In the x-ray imaging, the x-rays are sent on certain intensity through the measurable object and then the remaining intensity is measured using the x-ray detector. The detectors used in this thesis convert the remaining x-rays directly into electrical signals, which are then measured and finally processed into an image. We notice that the gained values behave according to an exponential model and use this knowledge to transform this into a nonlinear fitting problem. We study two linearization methods and three iterative methods. We examine the performance of the correction algorithms with both simulated and real stripe images. The results of the experiments show that although some of the fitting methods give better results in the least squares sense, the exponential prior leaves some visible line artefacts. This suggests that the methods can be further improved by applying suitable regularization method. We believe that this study is a good baseline for a better correction method.