VOIR: a volumetric image reconstruction algorithm based on Fourier techniques for inversion of the 3-D Radon transform

Low-dose cone-beam computed tomography reconstruction through a fast three-dimensional compressed sensing method based on the three-dimensional pseudo-polar fourier transform

Background:

Reconstruction of high quality two dimensional images from fan beam computed tomography (CT) with a limited number of projections is already feasible through Fourier based iterative reconstruction method. However, this article is focused on a more complicated reconstruction of three dimensional (3D) images in a sparse view cone beam computed tomography (CBCT) by utilizing Compressive Sensing (CS) based on 3D pseudo polar Fourier transform (PPFT).

Method:

In comparison with the prevalent Cartesian grid, PPFT re gridding is potent to remove rebinning and interpolation errors. Furthermore, using PPFT based radon transform as the measurement matrix, reduced the computational complexity.

Results:

In order to show the computational efficiency of the proposed method, we compare it with an algebraic reconstruction technique and a CS type algorithm. We observed convergence in <20 iterations in our algorithm while others would need at least 50 iterations for reconstructing a qualified phantom image. Furthermore, using a fast composite splitting algorithm solver in each iteration makes it a fast CBCT reconstruction algorithm. The algorithm will minimize a linear combination of three terms corresponding to a least square data fitting, Hessian (HS) Penalty and l1 norm wavelet regularization. We named it PP-based compressed sensing-HS-W. In the reconstruction range of 120 projections around the 360° rotation, the image quality is visually similar to reconstructed images by Feldkamp-Davis-Kress algorithm using 720 projections. This represents a high dose reduction.

Conclusion:

The main achievements of this work are to reduce the radiation dose without degrading the image quality. Its ability in removing the staircase effect, preserving edges and regions with smooth intensity transition, and producing high-resolution, low-noise reconstruction results in low-dose level are also shown.

An Exact and Fast CBCT Reconstruction via Pseudo-Polar Fourier Transform based Discrete Grangeat's Formula

The recent application of Fourier Based Iterative Reconstruction Method (FIRM) has made it possible to achieve high-quality 2D images from a fan beam Computed Tomography (CT) scan with a limited number of projections in a fast manner. The proposed methodology in this article is designed to provide 3D Radon space in linogram fashion to facilitate the use of FIRM with cone beam projections (CBP) for the reconstruction of 3D images in a sparse view angles Cone Beam CT (CBCT). For this reason, in the first phase, the 3D Radon space is generated using CBP data after discretization and optimization of the famous Grangeat's formula. The method used in this process involves fast Pseudo Polar Fourier transform (PPFT) based on 2D and 3D Discrete Radon Transformation (DRT) algorithms with no wraparound effects. In the second phase, we describe reconstruction of the objects with available Radon values, using direct inverse of 3D PPFT. The method presented in this section eliminates noises caused by interpolation from polar to Cartesian space and exhibits no thorn, V-shaped and wrinkle artifacts. This method reduces the complexity to for images of size n × n × n The Cone to Radon conversion (Cone2Radon) Toolbox in the first phase and MATLAB/ Python toolbox in the second phase were tested on three digital phantoms and experiments demonstrate fast and accurate cone beam image reconstruction due to proposed.

Compensating the intensity fall-off effect in cone-beam tomography by an empirical weight formula

The Feldkamp-David-Kress (FDK) algorithm is widely adopted for cone-beam reconstruction due to its one-dimensional filtered backprojection structure and parallel implementation. In a reconstruction volume, the conspicuous cone-beam artifact manifests as intensity fall-off along the longitudinal direction (the gantry rotation axis). This effect is inherent to circular cone-beam tomography due to the fact that a cone-beam dataset acquired from circular scanning fails to meet the data sufficiency condition for volume reconstruction. Upon observations of the intensity fall-off phenomenon associated with the FDK reconstruction of a ball phantom, we propose an empirical weight formula to compensate for the fall-off degradation. Specifically, a reciprocal cosine can be used to compensate the voxel values along longitudinal direction during three-dimensional backprojection reconstruction, in particular for boosting the values of voxels at positions with large cone angles. The intensity degradation within the z plane, albeit insignificant, can also be compensated by using the same weight formula through a parameter for radial distance dependence. Computer simulations and phantom experiments are presented to demonstrate the compensation effectiveness of the fall-off effect inherent in circular cone-beam tomography.

Volume fusion for two-circular-orbit cone-beam tomography

By using the Feldkamp-Davis-Kress (FDK) algorithm, we can efficiently produce a digital volume, called the FDK volume, from cone-beam data acquired along a circular scan orbit. Due to the insufficiency of the cone-beam data set, the FDK volume suffers from nonuniform reproduction exactness. Specifically, the midplane (on the scan-orbit plane) can be exactly reproduced, and the reproduction exactness of off-midplanes decreases as the distance from the midplane increases. We describe the longitudinal falling-off degradation by a hatlike function and the spatial distribution over the object domain by an exactness volume. With two orthogonal circular scan orbits, we can reconstruct two FDK volumes and generate two exactness volumes. We propose a volume fusion scheme to combine the two FDK volumes into a single volume. Let Va and Vb denote the two FDK volumes, let Ea and Eb denote the exactness volumes for orbits Gamma(a) and Gamma(b), respectively, then the volume fusion is defined by Vab=VaWa+VbWb, with Wa=Ea/(Ea+Eb) and Wb=1-Wa. In the result, the overall reproduction exactness of Vab is expected to outperform that of Va, or Vb, or (Va+Vb)/2. In principle, this volume-fusion scheme is applicable for general cone-beam tomography with multiple nonorthogonal and noncircular orbits.

High resolution X-ray computed tomography: an emerging tool for small animal cancer research

Dedicated high-resolution small animal imaging systems have recently emerged as important new tools for cancer research. These new imaging systems permit researchers to noninvasively screen animals for mutations or pathologies and to monitor disease progression and response to therapy. One imaging modality, X-ray microcomputed tomography (microCT) shows promise as a cost-effective means for detecting and characterizing soft-tissue structures, skeletal abnormalities, and tumors in live animals. MicroCT systems provide high-resolution images (typically 50 microns or less), rapid data acquisition (typically 5 to 30 minutes), excellent sensitivity to skeletal tissue and good sensitivity to soft tissue, particularly when contrast-enhancing media are employed. The development of microCT technology for small animal imaging is reviewed, and key considerations for designing small animal microCT imaging protocols are summarized. Recent studies on mouse prostate, lung and bone tumor models are overviewed.