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. 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). 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. 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.

Background: Accurate segmentation of pancreatic cancer tumors using positron emission tomography/computed tomography (PET/CT) multimodal images is crucial for clinical diagnosis and prognosis evaluation. However, deep learning methods for automated medical image segmentation require a substantial amount of manually labeled data, making it time-consuming and labor-intensive. Moreover, addition or simple stitching of multimodal images leads to redundant information, failing to fully exploit the complementary information of multimodal images. Therefore, we developed a semisupervised multimodal network that leverages limited labeled samples and introduces a cross-fusion and mutual information minimization (MIM) strategy for PET/CT 3D segmentation of pancreatic tumors. Methods: Our approach combined a cross multimodal fusion (CMF) module with a cross-attention mechanism. The complementary multimodal features were fused to form a multifeature set to enhance the effectiveness of feature extraction while preserving specific features of each modal image. In addition, we designed an MIM module to mitigate redundant high-level modal information and compute the latent loss of PET and CT. Finally, our method employed the uncertainty-aware mean teacher semi-supervised framework to segment regions of interest from PET/CT images using a small amount of labeled data and a large amount of unlabeled data. Results: We evaluated our combined MIM and CMF semisupervised segmentation network (MIM-CMFNet) on a private dataset of pancreatic cancer, yielding an average Dice coefficient of 73.14%, an average Jaccard index score of 60.56%, and an average 95% Hausdorff distance (95HD) of 6.30 mm. In addition, to verify the broad applicability of our method, we used a public dataset of head and neck cancer, yielding an average Dice coefficient of 68.71%, an average Jaccard index score of 57.72%, and an average 95HD of 7.88 mm. Conclusions: The experimental results demonstrate the superiority of our MIM-CMFNet over existing semisupervised techniques. Our approach can achieve a performance similar to that of fully supervised segmentation methods while significantly reducing the data annotation cost by 80%, suggesting it is highly practicable for clinical application.