Constrained sinogram restoration for limited-angle tomography

An Improved Extrapolation Scheme for Truncated CT Data Using 2D Fourier-Based Helgason-Ludwig Consistency Conditions

“…Second, the 2D Fourier transform via FFT is computationally more efficient than other transforms (e.g., the Chebyshev-Fourier transform [16] or Lagrange-Fourier transform [11]). This allows us to develop more efficient sinogram recovery schemes, as demonstrated in this paper.…”

“…The HL consistency conditions play an important role in image reconstruction from imperfect projection data (e.g., due to noise, motion, and truncation) since these projections no longer satisfy the HL conditions. Related work uses HL conditions to estimate motion parameters directly from sinograms [8–10] or to solve the problem of limited angle tomography using a variational formulation that incorporates HL conditions [11]. In PET/SPECT, the HL consistency conditions were also used for attenuation correction if no transmission data is available [12].…”

“…Several applications using this Fourier property of a sinogram can be found in [8, 20–23]. In this work, we theoretically prove the equivalence between the HL consistency conditions and the Fourier property of a sinogram and show the advantages of applying these Fourier-based consistency conditions: first, an infinite number of conditions are considered; and second, 2D Fourier transform via FFT is computationally more efficient than the Chebyshev-Fourier transform [16] or Lagrange-Fourier transform [11]. These features allow us to develop an efficient data extrapolation method by optimization of a cost function based on the Fourier-based HL conditions.…”

A platform‐independent method to reduce CT truncation artifacts using discriminative dictionary representations

“…To reduce CT truncation artifacts, a variety of data extrapolation methods have been developed to enable smoother transitions of the projection data across the boundary of the SFOV. The data extrapolation process is usually guided by certain a priori knowledge about the image object and the CT system, including the zeroth‐order Helgason–Ludwig (HL) condition, the mass conservation of projection data, higher order HL condition, sinogram decomposition method, and leveraging truncation‐free projection data from prior CT exams . The key to these extrapolation methods is to replace the missing projection data, so that the projection data can fall smoothly to zero, and the assumption of compact support for the image object can be satisfied …”

Level-set reconstruction algorithm for ultrafast limited-angle X-ray computed tomography of two-phase flows

“…It is also relevant for extending the measurement principle to two-plane [3] and multi-plane (threedimensional CT) [4] approaches, in which the axial offset between the detector arc and the X-ray source path is no longer acceptable due to the extended target geometry. Different approaches [5,6] have shown that it is difficult, if not impossible, to create a reconstruction algorithm that is generally applicable to those limited-angle problems in the method of suppressing the artefacts appearing when standard reconstruction methods are applied. Only a reduction of the artefacts by optimizing the geometry is feasible [7].…”