Computed tomography (CT) technology is widely used in medical imaging, industrial non-destructive testing, and archaeological exploration. However, its application is often limited by issues such as high radiation doses or long scanning time. This paper utilizes the segmental limited-angle (SLA) sampling strategy to address these issues. However, SLA projections inherit limited-angle sampling properties, and shading artifacts still exist in the reconstructed images. To address this issue, we introduce the L1/L2 ratio of image gradients as a regularization term into SLA CT to construct a reconstruction model. The L1/L2 ratio is scale-invariant and can better approximate the L0 norm, shows great potential for improving image quality. To solve this model, we propose an improved L1/L2 minimization algorithm. First linearize the data fidelity term, and then use the Fast Fourier Transform (FFT) to accelerate the computation process. Finally, we employ the alternating direction method to obtain the reconstructed image. Numerical simulations and real CT data experiments demonstrate that the L1/L2 method outperforms other competing methods, and it can effectively preserve image structures and some details.
PontoneGScafuriSManciniME, et al.Role of computed tomography in COVID-19. J Cardiovasc Comput Tomogr2021; 15: 27–36.
2.
DanalaGRayBDesaiM, et al.Developing new quantitative CT image markers to predict prognosis of acute ischemic stroke patients. J Xray Sci Technol2022; 30: 459–475.
3.
HanHGaoHXingL. Low-dose 4D cone-beam CT via joint spatiotemporal regularization of tensor framelet and nonlocal total variation. Phy Med Biol2017; 62: 6408–6427.
4.
SahuHPKashyapR. Fine_denseiganet: automatic medical image classification in chest CT scan using hybrid deep learning framework. Int J Image Graph2025; 25: 2550004.
5.
SchrommTBeckmannFMoosmannJ, et al.Challenges in non-destructive X-ray CT testing of riveted joints in the automotive industry. Discover Appl Sci2024; 6: 333.
6.
HaY-SKwonJ-BYangW-J, et al.Application of Industrial 3D X-Ray CT(Computed Tomography) to Improve Reliability of Additive Manufacturing Technology. In: ISOPE International Ocean and Polar Engineering Conference, 2024.
FrancescoAMichela DeBMariaS, et al.X-ray computed microtomography: a non-invasive and time-efficient method for identifying and screening Roman copper-based coins. J Cultural Heritage2024; 66: 436–443.
9.
PicanoEVanoE. Updated estimates of radiation risk for cancer and cardiovascular disease: implications for cardiology practice. J Clin Med2024; 13: 2066.
10.
ShbeerA. Radiation in the intensive care units: a review of staff knowledge, practices, and radiation exposure. J Radiat Res Appl Sci2024; 17: 100849.
11.
YananWYuWPengL, et al.A directional relative TV algorithm for sparse-view CT reconstruction. J Xray Sci Technol2025; 33: 866–878.
12.
GenweiMDimengXShusenZ. Multi-domain information fusion diffusion model (MDIF-DM) for limited-angle computed tomography. J Xray Sci Technol2025; 33: 935–944.
13.
AbbasSLeeTShinS, et al.Effects of sparse sampling schemes on image quality in low-dose CT. Med Phys2013; 40: 111915.
14.
SidkyEYKaoC-MPanX. Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT. J Xray Sci Technol2006; 14: 119–139.
15.
SidkyEYPanX. Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys Med Biol2008; 53: 4777–4807.
16.
DengXZhaoXLiM, et al.Limited-angle CT reconstruction with generalized shrinkage operators as regularizers. Inverse Problems Imag2021; 15: 1287.
17.
FerreiraLABeraldoRGSuyamaR, et al.Deep image prior with sparsity constraint for limited-angle computed tomography reconstruction. Appl Math Modern Chall2023; 1: 105–125.
18.
LiXChenZXingY. Multi-segment limited-angle CT reconstruction via a BM3D filter. In: 2012 IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC), 2012, pp.2390–2394.
19.
GongCZengLGuoY, et al.Multiple limited-angles computed tomography reconstruction based on multi-direction total variation minimization. Rev Sci Instrum2018; 89: 125121.
20.
GongCShenZHeY. Segmental limited-angle CT reconstruction based on image structural prior. J Xray Sci Technol2022; 30: 1–28.
21.
SongQGongC. Image reconstruction method for incomplete CT projection based on self-guided image filtering. Med Biol Eng Comput2024; 62: 2101–2116.
22.
WangHGongC. Self-guided image filtering reconstruction algorithm based on the ASD-POCS algorithm framework. Chin J Stereol Image Anal2024; 29: 303–310.
GongCSongQLiuJ. Image reconstruction method for segmental limited-angle CT based on coupled relative structure. Appl Math Model2025; 144: 116066.
25.
RickC. Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Process Lett2007; 14: 707–710.
26.
ShiHWangJ. Improved sufficient condition for L1-L2-minimization on cumulative coherence. IEEE Access2024; 12: 89707–89712.
27.
LiPChenWGeH, et al.L1-αL2 minimization methods for signal and image reconstruction with impulsive noise removal. Inverse Prob2020; 36: 055009.
28.
PengLHuanminGPengboG. Signal and image reconstruction with tight frames via unconstrained L1-αL2-analysis minimizations. Signal Process2023; 203: 108755.
29.
YifeiLMingY. Fast L1-L2 minimization via a proximal operator. J Sci Comput2018; 74: 767–785.
30.
LouYZengTOsherS, et al.A weighted difference of anisotropic and isotropic total variation model for image processing. SIAM J Imag Sci2015; 8: 1798–1823.
31.
WangCZengLYuW, et al.Existence and convergence analysis of L0 and L2 regularizations for limited-angle CT reconstruction. Inverse Problems Imag2018; 12: 545–572.
32.
YuWWangCHuangM. Edge-preserving reconstruction from sparse projections of limited-angle computed tomography using L0-regularized gradient prior. Rev Sci Instrum2017; 88: 043703.
33.
RahimiYWangCDongH, et al.A scale-invariant approach for sparse signal recovery. SIAM J Sci Comput2019; 41: A3649–A3672.
34.
ChaoWMingYYaghoubR, et al.Accelerated schemes for the L1/L2 minimization. IEEE Trans Signal Process2020; 68: 2660–2669.
35.
TaoM. Minimization of L1 over L2 for sparse signal recovery with convergence guarantee. SIAM J Sci Comput2022; 44: A770–A797.
36.
ChowdhuryMRWangCLouY. Poissonian Image Restoration Via the L1/L2-Based Minimization. J Sci Comput2024; 101: 17.
37.
ChaoWMinTJamesN, et al.Limited-angle CT reconstruction via the L1/L2 minimization. SIAM J Imag Sci2021; 14: 749–777.
38.
QinCChenJGongC. Limited-angle CT reconstruction by minimizing L1 over L2 based on linearized alternating direction method. Signal Image Video Process2025; 19: 1149.
39.
ZhuRZhouYPangZ. Limited-Angle CT image reconstruction based on weighted total variation-type L1/L2 regularization. Chin J Stereol Image Anal2025; 30: 056–069.
40.
WangYYangJYinW, et al.A new alternating minimization algorithm for total variation image reconstruction. SIAM J Imag Sci2008; 1: 248–272.
41.
LinZLeiZXuanqinM, et al.FSIM: a feature similarity Index for image quality assessment. IEEE Trans Image Process2011; 20: 2378–2386.
