Inverse Radon transform without singularity for rays with a point focus

Abstract

Background: The need to reconstruct images from their projections has been repeated many times as a means of studying an object in a wide variety of fields of science, technology and medicine. The basis of this method is the penetration through object of beams under different angles and the acquisition of a shadow image on the surface sensitive to these rays. Since that the tissues and bones have different absorption densities from such projections it is possible to get a reasonably accurate idea of the presence of pathological formations or lesions. Despite all the advantages of tomography, it has disadvantages. One of the most serious is the exceedance of radiation for humans. Therefore, there are several options for reducing the burden on the patient, one of which is the use of tomosynthesis instead of CT scanning. Tomosynthesis occupies an average position in informativeness between computer tomography and radiology not much higher than the dose of the latter. As a result, work is underway worldwide to improve the tomosynthesis method to increase the number of diseases that can be diagnosed by this method and to improve the quality of the images obtained. Objectives: Defines the efficiency of the image recovery method when using the Radon transform in general form compared to classical methods. Materials and methods: Mathematical physics methods for reconstructing medical images, namely the Fourier transform in the polar coordinate system and the Radon transform. Results: As a result of the work done, an expression for the reverse Radon transform was obtained and the work of the tomograph with point focus of X-ray rays was modeled. When comparing different reconstruction techniques with the original image, the Radon transform is generally more accurate. Conclusions: Despite the considerable increase in the time of reconstruction computation, about three times, this method has practical advantages in the case of detection of pathologies that only develop and have no clear boundaries or in the case of detection of small objects.