Fully Automatic Sliding Motion Compensated and Simultaneous 4D-CBCT via Bilateral Filtering

PurposeTo incorporate the bilateral filtering into the Deformable Vector Field (DVF) based 4D-CBCT reconstruction for realizing a fully automatic sliding motion compensated 4D-CBCT.Materials and MethodsInitially, a motion compensated simultaneous algebraic reconstruction technique (mSART) is used to generate a high quality reference phase (e.g. 0% phase) by using all phase projections together with the initial 4D-DVFs. The initial 4D-DVF were generated via Demons registration between 0% phase and each other phase image. The 4D-DVF will then kept updating by matching the forward projection of the deformed high quality 0% phase with the measured projection of the target phase. The loss function during this optimization contains an projection intensity difference matching criterion plus a DVF smoothing constrain term. We introduce a bilateral filtering kernel into the DVF constrain term to estimate the sliding motion automatically. The bilateral filtering kernel contains three sub-kernels: 1) an spatial domain Guassian kernel; 2) an image intensity domain Guassian kernel; and 3) a DVF domain Guassian kernel. By choosing suitable kernel variances, the sliding motion can be extracted. A non-linear conjugate gradient optimizer was used. We validated the algorithm on a non-uniform rotational B-spline based cardiac-torso (NCAT) phantom and four anonymous patient data. For quantification, we used: 1) the Root-Mean-Square-Error (RMSE) together with the Maximum-Error (MaxE); 2) the Dice coefficient of the extracted lung contour from the final reconstructed images and 3) the relative reconstruction error (RE) to evaluate the algorithm's performance.ResultsFor NCAT phantom, the motion trajectory's RMSE/MaxE are 0.796/1.02 mm for bilateral filtering reconstruction; and 2.704/4.08 mm for original reconstruction. For patient pilot study, the 4D-Dice coefficient obtained with bilateral filtering are consistently higher than that without bilateral filtering. Meantime several image content such as the rib position, the heart edge definition, the fibrous structures all has been better corrected with bilateral filtering.ConclusionWe developed a bilateral filtering based fully automatic sliding motion compensated 4D-CBCT scheme. Both digital phantom and initial patient pilot studies confirmed the improved motion estimation and image reconstruction ability. It can be used as a 4D-CBCT image guidance tool for lung SBRT treatment.

Dynamic Error Correction of Filament Thermocouples with Different Structures of Junction based on Inverse Filtering Method

Since filament thermocouple is limited by its junction structure and dynamic characteristics, the actual heat conduction process cannot be reproduced during the transient thermal shock. In order to solve this problem, we established a thermocouple dynamic calibration system with laser pulse as excitation source to transform the problem of the restoring excitation source acting on the surface temperature of thermocouple junction into the problem of solving the one-dimensional (1D) inverse heat conduction process, proposed a two-layer domain filtering kernel regularization method for double conductors of thermocouple, analyzed the factors causing unstable two-layer domain solution, and solved the regular solution of two-layer domain by the filtering kernel regularization strategy. By laser narrow pulse calibration experiment, we obtained experimental samples of filament thermocouples with two kinds of junction structures, butt-welded and ball-welded; established error estimation criterion; and obtained the optimal filtering kernel parameters by the proposed regularization strategy, respectively. The regular solutions solved for different thermocouples were very close to the exact solution under the optimal strategy, indicating that the proposed regularization method can effectively approach the actual surface temperature of the thermocouple junction.

Energy Transfer in Incompressible Magnetohydrodynamics: The Filtered Approach

We develop incompressible magnetohydrodynamic (IMHD) energy budget equations witha spatial filtering kernel and estimate the scaling of the structure functions. The Politano-Pouquetlaw is recovered as an upper bound on the scale-to-scale energy transfer. The primary result ofthis work is the relation of the scaling of IMHD invariants. It can be produced by hypothesizing ascale-independent energy transfer rate. These results have relevance in plasma regimes where theapproximations of IMHD are justified. We measure structure functions with solar wind data and findsupport for the relations.

AN ANALYTICAL INVERSION OF THE 180° EXPONENTIAL RADON TRANSFORM WITH A NUMERICALLY GENERATED KERNEL

This work presents an inversion algorithm for the exponential Radon transform (ERT) over 180° range of view angles. The algorithm can be applied to two-dimensional parallel beam geometry in single photon emission computed tomography. First the differentiation of the ERT over π is backprojected. A convolutional relation between this backprojected differentiation and the original image is then established. In order to invert the convolution relation, the least-squares method is utilized to obtain a numerically generated filtering kernel, which readily restores the original image. The advantages of the proposed algorithm are, first, it only requires half the view angles of the conventional inversion algorithm, second, it deals with truncation in ERT data in certain situations, and third, the numerically generated filtering kernel can be pre-calculated and stored for later applications. The algorithm is an analytical approach except for the pre-calculated inverse kernel.