FDK-Type Algorithms with No Backprojection Weight for Circular and Helical Scan CT

We develop two Feldkamp-type reconstruction algorithms with no backprojection weight for circular and helical trajectory with planar detector geometry. Advances in solid-state electronic detector technologies lend importance to CT systems with the equispaced linear array, the planar (flat panel) detectors, and the corresponding algorithms. We derive two exact Hilbert filtered backprojection (FBP) reconstruction algorithms with no backprojection weight for 2D fan-beam equispace linear array detector geometry (complement of the equi-angular curved array detector). Based on these algorithms, the Feldkamp-type algorithms with no backprojection weight for 3D reconstruction are developed using the standard heuristic extension of the divergent beam FBP algorithm. The simulation results show that the axial intensity drop in the reconstructed image using the FDK algorithms with no backprojection weight with circular trajectory is similar to that obtained by using Hu's and T-FDK, algorithms. Further, we present efficient algorithms to reduce the axial intensity drop encountered in the standard FDK reconstructions in circular cone-beam CT. The proposed algorithms consist of mainly two steps: reconstruction of the object using FDK algorithm with no backprojection weight and estimation of the missing term. The efficient algorithms are compared with the FDK algorithm, Hu's algorithm, T-FDK, and Zhu et al.'s algorithm in terms of axial intensity drop and noise. Simulation shows that the efficient algorithms give similar performance in axial intensity drop as that of Zhu et al.'s algorithm while one of the efficient algorithms outperforms Zhu et al.'s algorithm in terms of computational complexity

Adaptive Variable Density Sampling Based on Knapsack Problem for Fast MRI

This paper presents a novel heuristic approach to generate a variable density sampling (VDS) pattern for fast MRI data acquisition, based on the principle of Knapsack problem. MR images are known to exhibit weak sparsity in Fourier domain. This sparsity has been exploited to devise faster k-space sampling schemes by acquiring lesser samples while using Compressed Sensing reconstruction techniques to reconstruct high quality MR images. The entire range of distribution of the magnitude of k-space is divided into fixed/variable bin widths and draw samples from these bins according to a cost criterion satisfying the undersampling factor. This will facilitate sampling the k-space coefficients by preserving the energy content for the desired undersampling factor and do away with the deterministic central region sampling resulting in a VDS method with a correlation to the magnitude spectrum of the reference image scan. Knapsack principle is used to select the relevant bins. The method is also devoid of parameter tuning, yielding significant good results at both the lower and higher under sampling ratios

Image reconstruction with laterally truncated projections in helical cone-beam CT: Linear prediction based projection completion techniques

Lateral or transaxial truncation of cone-beam data can occur either due to the field of view limitation of the scanning apparatus or iregion-of-interest tomography. In this paper, we Suggest two new methods to handle lateral truncation in helical scan CT. It is seen that reconstruction with laterally truncated projection data, assuming it to be complete, gives severe artifacts which even penetrates into the field of view. A row-by-row data completion approach using linear prediction is introduced for helical scan truncated data. An extension of this technique known as windowed linear prediction approach is introduced. Efficacy of the two techniques are shown using simulation with standard phantoms. A quantitative image quality measure of the resulting reconstructed images are used to evaluate the performance of the proposed methods against an extension of a standard existing technique

Estimation of Small Motion for Dynamic X-Ray Computed Tomography Using a General Motion Model and Moments of Projections

We propose a method for estimation of general (non-rigid) small motion for dynamic computed tomography (CT). In the proposed method we estimate motion parameters of the general motion model from the moments of the dynamic projections, inspired by the Helgason-Ludwig consistency conditions. The non-linear problem of solving a system involving composition of functions is dealt with in the Fourier transform space where it simplifies into a problem involving multiplicatively separable functions. The system is then linearized to solve for object motion. Numerical simulation results are shown for the proposed method for fan-beam geometry. The numerical simulation results show good agreement between estimated and true motion. The proposed method is X-ray dose efficient and does not need other aids such as gating or fiducidal markers

Evaluation of 2D image reconstruction using fan-beam FBP algorithm with no backprojection weight from WLP completed truncated projection data

This paper presents the image reconstruction using the fan-beam filtered backprojection (FBP) algorithm with no backprojection weight from windowed linear prediction (WLP) completed truncated projection data. The image reconstruction from truncated projections aims to reconstruct the object accurately from the available limited projection data. Due to the incomplete projection data, the reconstructed image contains truncation artifacts which extends into the region of interest (ROI) making the reconstructed image unsuitable for further use. Data completion techniques have been shown to be effective in such situations. We use windowed linear prediction technique for projection completion and then use the fan-beam FBP algorithm with no backprojection weight for the 2-D image reconstruction. We evaluate the quality of the reconstructed image using fan-beam FBP algorithm with no backprojection weight after WLP completion

Artificial Bee Colony (ABC) based Variable Density Sampling Scheme for CS-MRI

The self-sustained dynamics of the bee population in nature is a result of their hierarchical working culture, efficient organizing skills and unique highly developed foraging ability, which enables them to interact effectively among each other as well as with their environment. In this paper, a novel algorithm utilizing the bee's swarm intelligence, and its heuristics based on quality and quantity of food sources (nectars) is proposed to generate a variable density sampling (VDS) scheme lOr compressive sampling (CS) based fast NMI data acquisition. The algorithm uses the scout-bees for global random selection process which is further fine-tuned by employed and onlooker-bees who forage locally in the neighborhood giving prime importance to points possessing high fitness values (or high energy) usually located around the center of k-space. The algorithm introduces the concept of searching for the high quality lOod sources in annular regions, called as bins, of varying widths. Retrospective CS-MRI simulations show that the proposed k-ABC based VDS scheme performs significantly better than other sampling schemes