PURPOSE: MRI-based intravoxel incoherent motion (IVIM) and apparent diffusion coefficient (ADC) parameters evaluate molecular diffusion and microvascular perfusion. This study assessed their utility in esophageal squamous cell carcinoma (ESCC) staging, compared different measurement approaches, and explored their predictive value for surgical staging. METHODS: Eighty prospectively enrolled ESCC patients (61 males, 19 females; median age 70 years) from February 2020 to August 2020 underwent 3.0T IVIM-DWI with respiratory-triggered and fat saturation techniques. Tumor ADC and IVIM parameters were calculated (b-values: 0-1000 s/mm²) for maximum-diameter slices and whole-volume regions of interest (ROI), and their correlations with T (tumor)/N (lymph node involvement) staging were analyzed. RESULTS: Full-volume measurements demonstrated higher interobserver reproducibility than single-slice measurements. For T staging, tumors with lower single-slice ADC_max and D_min values, as well as lower whole-volume ADC_std, were more likely to present with advanced stages (all p < 0.05). Parameters derived from the maximum-diameter slice provided higher diagnostic accuracy for T-stage discrimination compared with whole-volume analysis (AUC 0.75 vs. 0.70). For N staging, single-slice D_mean was associated with nodal involvement, while whole-volume analysis revealed that lower D_max, f_mean, f_min, and D*_std along with higher D*_min were correlated with lymph node metastasis, yielding better diagnostic performance (AUC 0.70 vs. 0.60). CONCLUSION: MRI-derived IVIM and ADC parameters provide non-invasive biomarkers for ESCC staging with the potential to guide preoperative decision-making, while exploring different ROI delineation strategies may further enhance research and clinical application.

Recently, deep unfolding networks (DUNs) based on optimization algorithms have received increasing attention, and their high efficiency has been confirmed by many experimental and theoretical results. Since this type of networks combines model-based traditional optimization algorithms, they have high interpretability. In addition, ordinary differential equations (ODEs) are often used to explain deep neural networks, and provide some inspiration for designing innovative network models. In this paper, we transform DUNs into first-order ODE forms, and propose a high-order numerical architecture for ODE-inspired deep unfolding networks. To the best of our knowledge, this is the first work to establish the relationship between DUNs and ODEs. Moreover, we take two representative DUNs as examples, apply our architecture to them and design novel DUNs. In theory, we prove the existence, uniqueness of the solution and convergence of the proposed network, and also prove that our network obtains a fast linear convergence rate. Extensive experiments verify the effectiveness and advantages of our architecture.

Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has attracted increasing attentions. A large number of experiments as well as some theories have proved the high efficiency of LISTA for solving sparse coding problems. However, existing LISTA methods are all serial connection. To address this issue, we propose a novel extragradient based LISTA (ELISTA), which has a residual structure and theoretical guarantees. Moreover, most LISTA methods use the soft thresholding function, which has been found to cause a large estimation bias. Therefore, we propose a thresholding function for ELISTA instead of soft thresholding. From a theoretical perspective, we prove that our method attains linear convergence. Through ablation experiments, the improvements of our method on the network structure and the thresholding function are verified in practice. Extensive empirical results verify the advantages of our method.

Recently, many stochastic variance reduced alternating direction methods of multipliers (ADMMs) (e.g., SAG-ADMM and SVRG-ADMM) have made exciting progress such as linear convergence rate for strongly convex (SC) problems. However, their best-known convergence rate for non-strongly convex (non-SC) problems is$\mathcal {O}(1/T)$as opposed to$\mathcal {O}(1/T^2)$of accelerated deterministic algorithms, where$T$is the number of iterations. Thus, there remains a gap in the convergence rates of existing stochastic ADMM and deterministic algorithms. To bridge this gap, we introduce a new momentum acceleration trick into stochastic variance reduced ADMM, and propose a novel accelerated SVRG-ADMM method (called ASVRG-ADMM) for the machine learning problems with the constraint$Ax + By = c$. Then we design a linearized proximal update rule and a simple proximal one for the two classes of ADMM-style problems with$B = \tau I$and$B\ne \tau I$, respectively, where$I$is an identity matrix and$\tau$is an arbitrary bounded constant. Note that our linearized proximal update rule can avoid solving sub-problems iteratively. Moreover, we prove that ASVRG-ADMM converges linearly for SC problems. In particular, ASVRG-ADMM improves the convergence rate from$\mathcal {O}(1/T)$to$\mathcal {O}(1/T^2)$for non-SC problems. Finally, we apply ASVRG-ADMM to various machine learning problems, e.g., graph-guided fused Lasso, graph-guided logistic regression, graph-guided SVM, generalized graph-guided fused Lasso and multi-task learning, and show that ASVRG-ADMM consistently converges faster than the state-of-the-art methods.