Structure-adaptive CBCT reconstruction using weighted total variation and Hessian penalties

Abstract

Abstract:The exposure of normal tissues to high radiation during cone-beam CT (CBCT) imaging increases the risk of cancer and genetic defects. Statistical iterative algorithms with the total variation (TV) penalty have been widely used for low dose CBCT reconstruction, with state-of-the-art performance in suppressing noise and preserving edges. However, TV is a first-order penalty and sometimes leads to the so-called staircase effect, particularly over regions with smooth intensity transition in the reconstruction images. A second-order penalty known as the Hessian penalty was recently used to replace TV to suppress the staircase effect in CBCT reconstruction at the cost of slightly blurring object edges. In this study, we proposed a new penalty, the TV-H, which combines TV and Hessian penalties for CBCT reconstruction in a structure-adaptive way. The TV-H penalty automatically differentiates the edges, gradual transition and uniform local regions within an image using the voxel gradient, and adaptively weights TV and Hessian according to the local image structures in the reconstruction process. Our proposed penalty retains the benefits of TV, including noise suppression and edge preservation. It also maintains the structures in regions with gradual intensity transition more successfully. A majorization-minimization (MM) approach was designed to optimize the objective energy function constructed with the TV-H penalty. The MM approach employed a quadratic upper bound of the original objective function, and the original optimization problem was changed to a series of quadratic optimization problems, which could be efficiently solved using the Gauss-Seidel update strategy. We tested the reconstruction algorithm on two simulated digital phantoms and two physical phantoms. Our experiments indicated that the TV-H penalty visually and quantitatively outperformed both TV and Hessian penalties.

Low-Dose CBCT Reconstruction Using Hessian Schatten Penalties

“…This seems to be a common limitation for the second-order penalties that has been observed in a previous study of the Hessian penalty [29]. Shi et al combined TV and Hessian penalties using a local structure adaptive strategy for CBCT reconstruction [30], where the associated objective function was not convex anymore and an alternative minimization method was used for the optimization process. A similar strategy can be used in the future to combine the HS penalty family with the TV penalty for 3D CBCT reconstruction to preserve both sharp edges and regions with smooth intensity transitions.…”

“…However, like most higher-order penalties, the Hessian penalty tends to slightly blur the edges of the reconstructed image. Shi et al [30] proposed a new penalty combining the TV and Hessian penalties in a structure-adaptive way to reconstruct CBCT images without introducing extra parameters. The proposed penalty can automatically adjust the weight parameters between TV and Hessian according to local image structures to suppress the staircase effect and preserve edges simultaneously.…”

Non-Blind Image Deblurring Method Using Shear High Order Total Variation Norm

“…In Ref. [13], the authors pointed out that high-order TV's ability to preserve edges became weaker compared with first-order TV regularization and tended to smoothen edges and other small details. Thus, hybrid models that combine higher-order TV with other regularization were proposed in many literatures [13][14][15] .…”

Low-Dose Cone-Beam CT Iterative Reconstruction via Total Variation and Gradient Total Variation

“…However, high-order penalties can effectively reduce the piecewise-constant effect, but might also introduce additional edge blurry. Besides those methods, other methods are further investigated for low-dose CBCT reconstruction, such as the dictionary learning [51], and Hessian Schatten penalties [52,53]. In addition, based on the deep learning methods [54,55] are also used for the CBCT reconstruction, and good results have been achieved.…”