Background: In order to reduce the radiation dose of CT (computed tomography), compressed sensing theory has been a hot topic since it provides the possibility of a high quality recovery from the sparse sampling data. Recently, the algorithm based on DL (dictionary learning) was developed to deal with the sparse CT reconstruction problem. However, the existing DL algorithm focuses on the minimization problem with the L2-norm regularization term, which leads to reconstruction quality deteriorating while the sampling rate declines further. Therefore, it is essential to improve the DL method to meet the demand of more dose reduction.
Methods: In this paper, we replaced the L2-norm regularization term with the L1-norm one. It is expected that the proposed L1-DL method could alleviate the over-smoothing effect of the L2-minimization and reserve more image details. The proposed algorithm solves the L1-minimization problem by a weighting strategy, solving the new weighted L2-minimization problem based on IRLS (iteratively reweighted least squares).
Results: Through the numerical simulation, the proposed algorithm is compared with the existing DL method (adaptive dictionary based statistical iterative reconstruction, ADSIR) and other two typical compressed sensing algorithms. It is revealed that the proposed algorithm is more accurate than the other algorithms especially when further reducing the sampling rate or increasing the noise.
Conclusion: The proposed L1-DL algorithm can utilize more prior information of image sparsity than ADSIR. By transforming the L2-norm regularization term of ADSIR with the L1-norm one and solving the L1-minimization problem by IRLS strategy, L1-DL could reconstruct the image more exactly.
Keywords: Dictionary learning; Image reconstruction; Iteratively reweighted least squares; L1-norm.