Ordered Subsets Convex Algorithm Research Articles

SU-GG-I-13: CBCT Total Variation Based Image Reconstruction from Limited Projections

PURPOSE: Cone beam computed tomography(CBCT) is commonly used for image‐guided external beam radiation therapy. There is interest and motivation to use a limited number of acquired projections to reconstruct the CBCT in order to reduce patient imagingdose; however, under these conditions filtered back projection (FBP) techniques typically used in CBCTreconstruction produce low quality CBCTimages. We propose to examine the application of a novel iterative reconstruction technique using total variation minimization for this problem. METHODS AND MATERIALS: A previously proposed adaptive steepest descent — projection onto convex set algorithm was modified with an ordered subset convex algorithm replacing the simultaneous algebraic reconstruction technique in the POCS step (ASD‐POCS‐OSC). ASD‐POCS‐OSC was used to reconstruct 60 projections of an anthropomorphic phantom uniformly spaced over 360 degrees to an image space of 512 × 512 × 200. Projections were acquired with an Elekta XVICBCTimagingsystem using the medium field of view with an offset detector panel. Reconstruction results were compared to imagesreconstructed with FBP for several image metrics. RESULTS: After one iteration the ASD‐POCS‐OSC images show improved edge definition, higher contrast‐to‐noise ratios, and decreased artifacts compared to the FBP reconstructed images. ASD‐POCS‐OSC reconstruction requires an increased computational burden and reconstruction time compared to FBP. CONCLUSION: Iterative reconstruction algorithms, such as ASD‐POCS‐OSC, yield reconstructed images with improved image quality compared to FBP algorithms. Iterative algorithms optimized for speed and performance may allow for the use of limited projection CBCTs to be used for patient setup on current clinical imaging devices. Supported in part by NCI T‐32 CA113267.

A faster ordered-subset convex algorithm for iterative reconstruction in a rotation-free micro-CT system

We present a faster iterative reconstruction algorithm based on the ordered-subset convex (OSC) algorithm for transmission CT. The OSC algorithm was modified such that it calculates the normalization term before the iterative process in order to save computational cost. The modified version requires only one backprojection per iteration as compared to two required for the original OSC. We applied the modified OSC (MOSC) algorithm to a rotation-free micro-CT system that we proposed previously, observed its performance, and compared with the OSC algorithm for 3D cone-beam reconstruction. Measurements on the reconstructed images as well as the point spread functions show that MOSC is quite similar to OSC; in noise-resolution trade-off, MOSC is comparable with OSC in a regular-noise situation and it is slightly worse than OSC in an extremely high-noise situation. The timing record shows that MOSC saves 25–30% CPU time, depending on the number of iterations used. We conclude that the MOSC algorithm is more efficient than OSC and provides comparable images.

Noise and resolution in images reconstructed with FBP and OSC algorithms for CT

This paper presents a comparison between an analytical and a statistical iterative reconstruction algorithm for computed transmission tomography concerning their noise and resolution performance. The reconstruction of two-dimensional images from simulated fan-beam transmission data is performed with a filtered back-projection (FBP) type reconstruction and an iterative ordered subsets convex (OSC) maximum-likelihood method. A special software phantom, which allows measuring the resolution and noise in a nonambiguous way, is used to simulate transmission tomography scans with different signal-to-noise ratios (SNR). The noise and modulation transfer function is calculated for FBP and OSC reconstruction at several positions, distributed over the field-of-view (FOV). The reconstruction with OSC using different numbers of subsets shows an inverse linear relation to the number of iterations that are necessary to reach a certain resolution and SNR, i.e., increasing the number of subsets by a factor x reduces the number of required iterations by the same factor. The OSC algorithm is able to achieve a nearly homogeneous high resolution over the whole FOV, which is not achieved with FBP. The OSC method achieves a lower level of noise compared with FBP at the same resolution. The reconstruction with OSC can save a factor of up to nine of x-ray dose compared with FBP in the investigated range of noise levels.

Parallel statistical image reconstruction for cone-beam x-ray CT on a shared memory computation platform

Statistical reconstruction methods offer possibilities of improving image quality as compared to analytical methods, but current reconstruction times prohibit routine clinical applications. To reduce reconstruction times we have parallelized a statistical reconstruction algorithm for cone-beam x-ray CT, the ordered subset convex algorithm (OSC), and evaluated it on a shared memory computer. Two different parallelization strategies were developed: one that employs parallelism by computing the work for all projections within a subset in parallel, and one that divides the total volume into parts and processes the work for each sub-volume in parallel. Both methods are used to reconstruct a three-dimensional mathematical phantom on two different grid densities. The reconstructed images are binary identical to the result of the serial (non-parallelized) algorithm. The speed-up factor equals approximately 30 when using 32 to 40 processors, and scales almost linearly with the number of cpus for both methods. The huge reduction in computation time allows us to apply statistical reconstruction to clinically relevant studies for the first time.