Iterative Reconstruction Algorithms Of Ultrasound Computer Tomography With Incomplete Projections

As one of modern medical imaging techniques, ultrasound computer tomography (UCT) has been widely used in many fields such as medical imaging and industrial non-invasion detection, which is due to the advantages as safety, various imaging modalities and low-cost when compared with X-ray computer tomography. In the practical UCT, incomplete projection problems occur quite frequently in condition of practical constraints due to the imaging hardware, scanning geometry, or ionizing radiation and so on. The incomplete projection may arise from various forms such as few-view projections, limited-angle projections and bad bins in the detector. When the projections are incomplete, reconstruction by using standard analytic algorithms will lead to distortion and artifact. Then we can use the iterative methods to deal with this problem, which convert the reconstruction problem into optimization problem and introduce the priori knowledge of the image to correct the reconstruction in the iterative process.To address the incomplete projection reconstruction in UCT, we mainly consider two aspects in this paper:first, obtain more information under the fixed sampling conditions; second, use the prior knowledge to reconstruct image after obtaining the incomplete projections. The main work and innovations are listed as follows:1. For the first aspect, we propose an entropy weighted non-uniform scanning algorithm. By the observation of frequency domain projecting image based on the Fourier diffraction projection theorem (FDPT), one can find that projection in frequency domain is not uniformly distributed when the spatial domain scanning angle is equispaced. However, this brings the information loss. We analyze the conditions under which the information lost most. Then, we define the information entropy of each scanning and propose a non-uniform scanning algorithm to maximize the amount of information under conditions of a fixed number of sampling points and scanning angles. The algorithm has five different kinds of the weighting vectors based on different weighting programs. The simulation result indicates that the algorithm proposed can improve the reconstruction quality.2. By using the limited extend nature of the image, we formulate the limited-angle reconstruction problem as an extrapolative problem of band-limited functions, and propose an iterative reprojection-reconstruction (IRR) algorithm using a modified Papoulis-Gerchberg (PG) iterative scheme. The proposed algorithm has two iterative update processes, one is the extrapolation of unknown data, and the other is the modification of the known noisy observation data. To deal with no convergence problem of the traditional PG algorithm in noisy situations, the proposed algorithm introduces scaling factors to control the two processes, respectively. The convergence of the algorithm is guaranteed, and the method of choosing the scaling factors is given with energy constraints.3. We propose two reconstruction algorithms based on the sparsity of the discrete gradient transform (DGT). In the CT field, total variation (TV), which is the l1-norm of the DGT, is widely used as regularization based on the compressive sensing (CS) theory. To overcome the TV model’s disadvantageous tendency of uniformly penalizing the image gradient and over smoothing the low-contrast structures, two iterative algorithms based on the l0-norm optimization of the DGT is proposed. To rise to the challenges introduced by the l0-norm DGT, the former uses a pseudo-inverse transform of DGT and adapts an iterative hard thresholding (IHT) algorithm; the latter uses the alternating direction method (ADM) to solve the unconstrained augmented Lagrangian function, which involves a hard thresholding method, a linearization and proximal points technique for each subproblem. The simulation demonstrates that these proposed algorithms can obviously improve the reconstruction quality.