Restoration of missing data in limited angle tomography based on Helgason-Ludwig consistency conditions

In limited angle tomography, missing data in an insufficient angular scan will cause streak artifacts in the reconstructed images. Correspondingly, in the frequency domain representation of the imaged object, a double wedge-shaped region is missing. In this paper, we perform a regression in sinogram domain and an image fusion in frequency domain to restore the missing data. We first convert the sinogram restoration problem into a regression problem based on the Helgason-Ludwig consistency conditions. Due to its severe ill-posedness, regression only partially recovers the correct frequency components, especially lower frequency components, and will introduce erroneous ones, particularly higher frequencies. Bilateral filtering is utilized to retain the most prominent high frequency components and suppress erroneous ones. Afterwards, a fusion in the frequency domain utilizes the restored frequency components to fill the missing double wedge region. The proposed method is evaluated in a parallel-beam study on both numerical and clinical phantoms. The root-mean-square errors of the reconstructed images decrease from 302 to 78 HU for the noise-free Shepp-Logan phantom, from 355 to 175 HU for the noisy Shepp-Logan phantom, and from 187 to 56 HU for the clinical data. The results show that our method is promising in streak reduction and intensity offset compensation in both noise-free and noisy situations.