Abstract We propose a novel way to incorporate morphology operators through structured regularization of machine learning models. Specifically, we introduce a feature map in the models that performs structured variable selection. The feature map is automatically processed by approximate morphology operators and is learned together with the model coefficients. Experiments were conducted with linear regression on both synthetic data, demonstrating that the proposed methods are effective in selecting groups of parameters with much less noise than baseline models, and on three-dimensional T1-weighted brain magnetic resonance images (MRI) for age prediction, demonstrating that the proposed methods enforce sparsity and select homogeneous regions of non-zero and relevant regression coefficients. The proposed methods improve interpretability in pattern analysis. The minimum size of features in the structured variable selection can be controlled by adjusting the structuring element in the approximate morphology operator, tailored to the specific study of interest. With these added benefits, the proposed methods still perform on par with commonly used variable selection and structured variable selection methods in terms of the coefficient of determination and the Pearson correlation coefficient.

Escape routing is a critical problem in PCB routing, and its quality dramatically affects the cost of the PCB design. Unlike the traditional escape routing that works mainly for the BGA with unique line width and space, this paper presents a high-performance escape routing algorithm to handle problems with variable design rules and multiple constraints. We first propose a novel obstacle-avoiding method to project pins to the boundary and construct a channel projection graph combined with a channel merging technique to handle complex irregular packages. We then construct a bi-projection graph and propose a matching-based hierarchical sequencing algorithm to consider manual constraints. We perform global routing for each pin/differential pair by congestion-avoiding path initializing and rip-up and reroute path optimizing. Finally, a length-aware detail routing algorithm is developed to optimize the line length while ensuring the differential pair constraints. The experimental results on industrial PCB instances show that our algorithm can achieve 100% routability without violating the design rules and constraints, while two state-of-the-art PCB routers, FreeRouting and Allegro, cannot complete escape routing.

Escape routing is a critical problem in PCB routing, and its quality greatly affects the PCB design cost. Unlike the traditional escape routing that works mainly for the BGA package with unique line width and space, this paper presents a high-performance escape routing algorithm to handle problems with variable design rules and manual constraints, including variable line widths/spaces, the neck mode of wires, and the pad entry for differential pairs. We first propose a novel obstacle-avoiding method to project pins to the boundary and construct a channel projection graph. We then construct a bi-projection graph and propose a matching-based hierarchical sequencing algorithm to consider manual constraints. We perform global routing for each pin/differential pair by congestion-avoiding path initialization and rip-up and reroute path optimization. Finally, we complete detailed routing in every face, ensuring the wire angle and pad entry constraints. Experimental results show that our algorithm can achieve 100% routability without any design rule violation for all given industrial PCB instances, while two state-of-the-art routers cannot complete routing.

Long-wave infrared (LWIR) images have important applications in retrieving land surface temperature. However, LWIR images are often inevitably suffered from stripe noise, a special type of spatial domain fixed pattern noise. This paper proposes a novel spectral separation algorithm for LWIR image destriping. Specifically, since the mid-wave infrared (MWIR) bands contain both radiant and reflective energy, we use MWIR as reference images to remove the stripe noise in the LWIR bands. We formulate the spectral separation problem as a convex optimization problem, where the difference between LWIR and the radiant component of MWIR, and the difference between the visible and near infrared (VNIR) image and the reflective component of MWIR are regularized to exploit the similarities between the corresponding bands. The obtained radiant component is then utilized to recover the LWIR band. Experimental results using Gaofen-5 datasets demonstrate that the proposed algorithm has good performance in removing the stripe noise.

Four-dimensional magnetic resonance imaging (4D-MRI) can provide 3D tissue properties and the temporal profiles at the same time. However, further applications of 4D-MRI is limited by the long acquisition time and motion artifacts. We introduce a regularized image reconstruction method to recover 4D MR images from their undersampled Fourier coefficients, named HDTV-LLR. We adopt the three-dimensional higher degree total variation and the local low-rank penalties to simultaneously exploit the spatial and temporal correlations of the dataset. In order to solve the resulting optimization problem efficiently, we propose a fast alternating minimization algorithm. The performance of the proposed method is demonstrated in the context of 4D cardiac MR images reconstruction with undersampling factors of 12 and 16. The proposed method is compared with iGRASP, and schemes using either low-rank or sparsity constraint alone. Numerical results show that the proposed method enables accelerated 4D-MRI with improved image quality and reduced artifacts.