Accelerated Barrier Optimization Compressed Sensing (ABOCS) for CT Reconstruction With Improved Convergence

Abstract

Recently, we proposed a new algorithm of accelerated barrier optimization compressed sensing (ABOCS) for iterative CT reconstruction. The previous implementation of ABOCS uses gradient projection (GP) with a Barzilai-Borwein (BB) step-size selection scheme (GP-BB) to search for the optimal solution. The algorithm does not converge stably due to its non-monotonic behavior. In this paper, we further improve the convergence of ABOCS using the unknown-parameter Nesterov (UPN) method and investigate the ABOCS reconstruction performance on clinical patient data. Comparison studies are carried out on reconstructions of computer simulation, a physical phantom and a head-and-neck patient. In all of these studies, the ABOCS results using UPN show more stable and faster convergence than those of the GPBB method and a state-of-theart Bregman-type method. As shown in the simulation study of the Shepp-Logan phantom, UPN achieves the same image quality as those of GPBB and the Bregman-type method, but reduces the iteration numbers by up to 50% and 90%, respectively. In the Catphan©600 phantom study, a high-quality image with relative reconstruction error (RRE) less than 3% compared to the fullview result is obtained using UPN with 17% projections (60 views). In the conventional filteredbackprojection (FBP) reconstruction, the corresponding RRE is more than 15% on the same projection data. The superior performance of ABOCS with the UPN implementation is further demonstrated on the head-and-neck patient. Using 25% projections (91 views), the proposed method reduces the RRE from 21% as in the FBP results to 7.3%. In conclusion, we propose UPN for ABOCS implementation. As compared to GPBB and the Bregman-type methods, the new method significantly improves the convergence with higher stability and less iterations.

GPU based parallel acceleration for fast C-arm cone-beam CT reconstruction

“…To acquire 3D volumetric images, several categories of algorithms are explored. One of the major category is the iterative algorithms such as ART combined with compress sensing theory using a Total Variation (TV) norm to regularize the cost function such as mentioned in [ 15 , 16 ]. The main challenge of such algorithms is the cost of calculation.…”

Low‐dose computed tomography scheme incorporating residual learning‐based denoising with iterative reconstruction

“…However, the performance of image denoising methods is limited due to the high complexity of noise and artefacts in LDCT images. Based on compressed sensing (CS), some methods [5,6] combine total variation (TV) with iterative reconstruction and achieve excellent performance. Unfortunately, CS-based methods are prone to be computational intensive due to a large number of required iterations, which limits their clinical applications.…”

“…The reconstruction stage is to calculate an image μ using measured projection data b. The CS-based iterative reconstruction can be formulated by solving such an optimisation problem [6]:…”

“…Shepp-Logan digital phantom is used to evaluate imaging performance. The error bound ɛ is set according to the Poisson noise variance of the projection data, and the step size α is selected using a Barzilai-Borwein method [6]. To find an optimal value of the early stopping iteration k, we compare the peak signal to noise ratio (PSNR) of the outputs of the reconstruction stage and denoising stage at different iterations, as shown in Fig.…”

“…During the offline training, the nested-ResNet is pre-trained on 90,000 image patches of size 40 × 40 extracted from an image dataset for Gaussian denoising [7] and then fine-tuned on LDCT images. Imaging performance of the proposed method is compared with the state-of-the-art methods including FBP, BM3D, denoising CNN (DnCNN) [7] and accelerated barrier optimisation CS (ABOCS) [6]. Fig.…”