2015/10/13 by Gaik Ambartsoumian, Souvik Roy, Ambartsoumian, Gaik +1 · 1 citation
Engineering · Mathematics · Medicine · #FOS: Mathematics #Medical Imaging Techniques and Applications #Numerical Analysis (math.NA) #Optical Imaging and Spectroscopy Techniques #Photoacoustic and Ultrasonic Imaging #Radiation Dose and Imaging #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.1510.03557
openalex publication_date 2015/10/13 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28
The article presents an efficient image reconstruction algorithm for single\nscattering optical tomography (SSOT) in circular geometry of data acquisition.\nThis novel medical imaging modality uses photons of light that scatter once in\nthe body to recover its interior features. The mathematical model of SSOT is\nbased on the broken ray (or V-line Radon) transform (BRT), which puts into\ncorrespondence to an image function its integrals along V-shaped piecewise\nlinear trajectories. The process of image reconstruction in SSOT requires\ninversion of that transform.\n We implement numerical inversion of a broken ray transform in a disc with\npartial radial data. Our method is based on a relation between the Fourier\ncoefficients of the image function and those of its BRT recently discovered by\nAmbartsoumian and Moon. The numerical algorithm requires solution of\nill-conditioned matrix problems, which is accomplished using a half-rank\ntruncated singular value decomposition method. Several numerical computations\nvalidating the inversion formula are presented, which demonstrate the accuracy,\nspeed and robustness of our method in the case of both noise-free and noisy\ndata.\n