Abstract
BackgroundThe sparse CT (Computed Tomography), inspired by compressed sensing, means to introduce a prior information of image sparsity into CT reconstruction to reduce the input projections so as to reduce the potential threat of incremental X-ray dose to patients’ health. Recently, many remarkable works were concentrated on the sparse CT reconstruction from sparse (limited-angle or few-view style) projections. In this paper we would like to incorporate more prior information into the sparse CT reconstruction for improvement of performance. It is known decades ago that the given projection directions can provide information about the directions of edges in the restored CT image. ATV (Anisotropic Total Variation), a TV (Total Variation) norm based regularization, could use the prior information of image sparsity and edge direction simultaneously. But ATV can only represent the edge information in few directions and lose much prior information of image edges in other directions.MethodsTo sufficiently use the prior information of edge directions, a novel MDATV (Multi-Direction Anisotropic Total Variation) is proposed. In this paper we introduce the 2D-IGS (Two Dimensional Image Gradient Space), and combined the coordinate rotation transform with 2D-IGS to represent edge information in multiple directions. Then by incorporating this multi-direction representation into ATV norm we get the MDATV regularization. To solve the optimization problem based on the MDATV regularization, a novel ART (algebraic reconstruction technique) + MDATV scheme is outlined. And NESTA (NESTerov’s Algorithm) is proposed to replace GD (Gradient Descent) for minimizing the TV-based regularization.ResultsThe numerical and real data experiments demonstrate that MDATV based iterative reconstruction improved the quality of restored image. NESTA is more suitable than GD for minimization of TV-based regularization.ConclusionsMDATV regularization can sufficiently use the prior information of image sparsity and edge information simultaneously. By incorporating more prior information, MDATV based approach could reconstruct the image more exactly.
Highlights
The sparse Computed tomography (CT) (Computed Tomography), inspired by compressed sensing, means to introduce a prior information of image sparsity into CT reconstruction to reduce the input projections so as to reduce the potential threat of incremental X-ray dose to patients’ health
The second model uses the sparsity coming from the subtraction of the reconstructed image from its prior image, such as Prior image constrained compressed sensing (PICCS) (Prior Image Constrained Compressed Sensing) [13], Prior image registered penalized likelihood estimation (PIRPLE) (Prior Image Registered Penalized Likelihood Estimation) [14,15] and Feature constrained compressed sensing (FCCS) (Feature Constrained Compressed Sensing) [16]
The aim of Multi-direction anisotropic total variation (MDATV) is to introduce into sparse CT reconstruction more prior information of edges, as the Anisotropic total variation (ATV) (Anisotropic Total Variation) does [31,32]
Summary
Review of ART + ATV ART The ART + ATV is proposed based on ART + TV method [11,12]. ART updates the estimated image iteratively. There are some horizontal artifacts in the restored image of ATV methods, which is caused by the unbalanced regularization, while the projection data are uniformly distributed. Discussions and conclusions The simulations and experiments both indicate that MDATV is a useful and robust regularization for the sparse CT reconstruction when the volume of the projection data. Using MDATV to incorporate more a prior information of the target images is valuable and gainful in practical applications, as shown in the real data experiment. This paper proposed the MDATV regularization to sufficiently use a prior information of projection directions and image sparsity in the sparse CT reconstruction.
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