Lossless compression of volumetric medical images is of paramount importance for clinical and research applications where data fidelity is essential. Traditional compression methods are often limited in efficiency due to rigid, handcrafted models. Conversely, deep neural network (DNN)-based compression methods, while effective, demand substantial computational resources, hindering deployment in resource-constrained settings. To address these challenges, we propose a novel tri-plane context tree (TCT)-based method for lossless volumetric medical image compression that delivers high performance without relying on DNNs or external training data. To exploit intra-slice and inter-slice redundancies, we introduce a compact tri-plane context representation that decomposes complex 3D context modeling into efficient 2D modeling on three orthogonal planes. By integrating this representation with a context tree framework, we develop an input-specific TCT model employing an adaptive binary tree structure. At each tree node, the model dynamically selects from a suite of tri-plane based predictors and contextual feature extractors, enabling data-adaptive context modeling tailored to local structural characteristics. Instead of offline training, we sample a subset of the input volume to learn the TCT model by optimizing the minimum description length (MDL) through iterative construction and pruning. With the learned TCT model, each pixel retrieves its corresponding context, computes the prediction residual using the predictor dictated by the context, and performs entropy encoding based on the associated histograms. Experimental results demonstrate that the proposed method achieves compression performance on par with recent DNN-based methods on multiple datasets, while maintaining low computational cost and fast coding speeds, making it highly applicable in practice.

Although a series of decoupled or single loop methods have been developed for reliability-based design optimization (RBDO) problems to improve the computational efficiency, it seems hard to extend these strategies to time-variant RBDO due to the complexity of the problems brought by the involvement of time. This paper proposes a new approach for time-variant reliability-based design optimization, expecting to provide an efficient tool for design of some complex structure under time-variant uncertainties. The main idea of the proposed method is the definition of the equivalent most probable point (EMPP). With the EMPP, the original time-variant RBDO problem can be transformed into an equivalent time-invariant RBDO problem formulated by performance measure approach (PMA). Hence, the existing PMA-based time-invariant RBDO methods can be applied to solve the equivalent problem. Therefore, those RBDO methods can be easily extended to time-variant RBDO problems, and hence the computational cost can be effectively reduced. Finally, two numerical examples and an engineering application are used to demonstrate the effectiveness of the proposed method.

In the process of long-term use, the uncertainty of an engineering structure often presents time-variant or dynamic characteristics due to the influence of stochastic loads and material performance degradations. In such a situation, the structural design optimization will involve an important problem of time-variant reliability-based design optimization (TRBDO). Performing TRBDO involves a nested optimization, which will lead to extremely low computational efficiency. In this paper, a single-loop approach (SLA) is proposed to convert the nested optimization in TRBDO into a sequence iterative process composed of the time-variant reliability analysis (TRA), constraint discretization, and design optimization. In each iteration step, the TRA method based on stochastic process discretization is first used to calculate the time-variant reliability of constraints; second, through introducing the concept of the target reliability index of discretized time period and proposing the corresponding algorithm, each time-variant constraint is discretized into a series of time-invariant constraints to formulate a conventional reliability-based design optimization problem. The approach exhibits a good comprehensive performance in terms of efficiency and convergence. The validity and practicality of the SLA are validated by two numerical examples and a design problem for the chassis of a self-balancing vehicle.