Compressed Sensing Based Conebeam Computed Tomography Image Reconstruction Methods

Computed tomography (CT) technique can get the internal information through anon-destructive way and has been widely used in a large number of applications inmedical diagnosis, industrial non-destructive detection and other fields. Because of itssmall size, light weight, mobility and flexiblity, cone-beam CT is extensively appliedto interventional surgery. However, cone-beam CT can not get sufficient projectiondata for exact reconstruction due to its sparse views. Thus the quality of thereconstructed image is not satisfied. Recent developments in compressed sensing haveenabled an accurate cone beam computed tomography (CBCT) reconstruction fromhighly undersampled projections. In this dissertation, we concentrate on thebackprojection weighted FDK algorithm, projection contraction based compressedsensing algorithm, a fast adaptive conjugate gradient projection algorithm to improvethe reconstruction accuracy and convergence speed. GPU is used to accelerate theimage reconstruction. The results are as follows:Cone beam artifacts increase along with the larger cone angle because thescanning trajectory of cone beam does not sufficiently satisfy data conditions. Aimedat the characteristics of missing data in Radon space, we propose a BackprojectionWeighted-FDK (BPW-FDK) algorithm for CBCT. A new backprojection weight ispresented to compensate for the missing data away from the rotating track forreconstruction region expansion. The images reconstructed from simulated noiselessprojections, projections with noise, and real projections from an internally developed3D scanner show that the proposed algorithm is able to sufficiently suppressartifacts away from the rotating track for large cone angle and provide more homogeneous image contrast. Its accuracy and speed make BPW-FDK algorithmsuitable for image reconstruction of real large CBCT.To solve the problem of image reconstruction of incomplete projection data fromcone-beam CT, a novel cone-beam CT reconstruction algorithm based onprojection-contraction method was proposed. Aiming at the non-monotonicconvergence of Gradient-Projection Barzilari-Borwein algorithm (GPBB), thepredictor-corrector feature of projection-contraction method was analyzed and wasincorporated into compressed sensing image reconstruction algorithm. The objectivefunction descent direction and the projection onto convex sets descent direction werecombined to correct the results of GPBB algorithm to improve the non-monotonicconvergence of GPBB algorithm. The experiments were conducted on simulatedprojection data and phantom scanning data. The simulated results show that, for25sampling angles, signal-to-noise ratio of images reconstructed by PCBB algorithm is9.4870db,9.8027db,3.6159db higher than those of images reconstructed by AdaptiveSteepest Descent-Projection Onto Convex Sets algorithm, projection contractionalgorithm and GPBB algorithm, respectively. The results of Phantom indicate thateven when a small amount of projections are acquired, the new algorithm caneffectively suppress strip artifacts and the reconstructed images show clear edge. Thealgorithm can greatly improve qualify of images reconstructed from few projectiondata.Recent developments in compressed sensing have enabled an accurate conebeam computed tomography (CBCT) reconstruction from highly undersampledprojections. However, gradient descent commonly used in these reconstructionmethods has a slow convergence speed. In this paper, we propose a novel CBCTreconstruction algorithm based on adaptive stepsize conjugate gradient (ASCG)method, which overcomes the drawback of the gradient descent methods. The CBCTimages are reconstructed by minimizing an objective function consisting of a datafidelity term and a TV-norm regularization term. While the data fidelity term uses l2norm to enforce the similarities between the measured projection data with theforward projections of reconstructed images, the penalty term uses Total variation(TV)-norm to enforce the piecewise constant property of the unknown object. Theobject function is minimized by conjugate gradient projection with the stepsizeanalytically calculated and adaptively changed at each iteration. The line searchtechnique is avoided to lessen the computation time. The Forbild numerical phantom is used to evaluate the performance of ASCG. Image relative error of reconstructedimages and computation efficiency were assessed and the behavior of ASCG arecompared with simultaneous algebraic reconstruction technique (SART), gradientprojection Barzilai-Borwein (GPBB) and another conjugate gradient projection usingfixed stepsize which is referred to FSCG. Under the condition of50-view projections,the ASCG algorithm showed convergence about600iterations whereas otheralgorithms need more than1000iterations to reconstruct the Forbild phantom image.For the same number of iteration, the computation time of ASCG is less than half ofthose of GPBB algorithm. we propose a novel adaptive stepsize conjugate gradientprojection algorithm for sparse-view CBCT reconstruction. Compared to GPBBalgorithm, ASCG algorithm has better performance both in convergence speed andreconstruction accuracy. These advantages have been demonstrated on Forbildphantom studies.To accelerate the Parker-FDK algorithm and SART for speedy and quality CTreconstruction by exploiting CUDA-enabled GPU, these techniques are proposed:(1)optimizing thread block size,(2) maximizing data reuse on constant memory andshared memory,(3) exploiting texture memory interpolation capability to increaseefficiency, and (4) using multiply GPUs. Two core techniques are proposed to useSART into the CUDA architecture:(1) a ray-driven projection along with hardwareinterpolation, and (2) a voxel-driven back-projection that can avoid redundantcomputation by combining CUDA shared memory. Extensive experimentsdemonstrate the proposed techniques can provide faster reconstruction with satisfiedimage quality.