arXiv subjects

Lei Ren

Publications and source records attributed to Lei Ren.

58 records · Page 4Linked to original sources

arXiv2020

Dissecting a square into congruent polygons

We study the dissection of a square into congruent convex polygons. Yuan \emph{et al.} [Dissecting the square into five congruent parts, Discrete Math. \textbf{339} (2016) 288-298] asked whether, if the number of tiles is a prime number $\geq 3$, it is true that the tile must be a rectangle. We conjecture that the same conclusion still holds even if the number of tiles is an odd number $\geq 3$. Our conjecture has been confirmed for triangles in earlier works. We prove that the conjecture holds if either the tile is a convex $q$-gon with $q\geq 6$ or it is a right-angle trapezoid.

math.CO↗

arXiv2020

Intensity Non-uniformity Correction in MR Imaging Using Residual Cycle Generative Adversarial Network

Purpose: Correcting or reducing the effects of voxel intensity non-uniformity (INU) within a given tissue type is a crucial issue for quantitative MRI image analysis in daily clinical practice. In this study, we present a deep learning-based approach for MRI image INU correction. Method: We developed a residual cycle generative adversarial network (res-cycle GAN), which integrates the residual block concept into a cycle-consistent GAN (cycle-GAN). In cycle-GAN, an inverse transformation was implemented between the INU uncorrected and corrected MRI images to constrain the model through forcing the calculation of both an INU corrected MRI and a synthetic corrected MRI. A fully convolution neural network integrating residual blocks was applied in the generator of cycle-GAN to enhance end-to-end raw MRI to INU corrected MRI transformation. A cohort of 30 abdominal patients with T1-weighted MR INU images and their corrections with a clinically established and commonly used method, namely, N4ITK were used as a pair to evaluate the proposed res-cycle GAN based INU correction algorithm. Quantitatively comparisons were made among the proposed method and other approaches. Result: Our res-cycle GAN based method achieved higher accuracy and better tissue uniformity compared to the other algorithms. Moreover, once the model is well trained, our approach can automatically generate the corrected MR images in a few minutes, eliminating the need for manual setting of parameters. Conclusion: In this study, a deep learning based automatic INU correction method in MRI, namely, res-cycle GAN has been investigated. The results show that learning based methods can achieve promising accuracy, while highly speeding up the correction through avoiding the unintuitive parameter tuning process in N4ITK correction.

physics.med-ph↗

arXiv2018

Iterative Inversion of Deformation Vector Fields with Feedback Control

Purpose: Often, the inverse deformation vector field (DVF) is needed together with the corresponding forward DVF in 4D reconstruction and dose calculation, adaptive radiation therapy, and simultaneous deformable registration. This study aims at improving both accuracy and efficiency of iterative algorithms for DVF inversion, and advancing our understanding of divergence and latency conditions. Method: We introduce a framework of fixed-point iteration algorithms with active feedback control for DVF inversion. Based on rigorous convergence analysis, we design control mechanisms for modulating the inverse consistency (IC) residual of the current iterate, to be used as feedback into the next iterate. The control is designed adaptively to the input DVF with the objective to enlarge the convergence area and expedite convergence. Three particular settings of feedback control are introduced: constant value over the domain throughout the iteration; alternating values between iteration steps; and spatially variant values. We also introduce three spectral measures of the displacement Jacobian for characterizing a DVF. These measures reveal the critical role of what we term the non-translational displacement component (NTDC) of the DVF. We carry out inversion experiments with an analytical DVF pair, and with DVFs associated with thoracic CT images of 6 patients at end of expiration and end of inspiration. Results: NTDC-adaptive iterations are shown to attain a larger convergence region at a faster pace compared to previous non-adaptive DVF inversion iteration algorithms. By our numerical experiments, alternating control yields smaller IC residuals and inversion errors than constant control. Spatially variant control renders smaller residuals and errors by at least an order of magnitude, compared to other schemes, in no more than 10 steps. Inversion results also show remarkable quantitative agreement with analysis-based predictions. Conclusion: Our analysis captures properties of DVF data associated with clinical CT images, and provides new understanding of iterative DVF inversion algorithms with a simple residual feedback control. Adaptive control is necessary and highly effective in the presence of non-small NTDCs. The adaptive iterations or the spectral measures, or both, may potentially be incorporated into deformable image registration methods.

cs.CV↗

arXiv2012

Terahertz and Infrared Spectroscopy of Gated Large-Area Graphene

We have fabricated a centimeter-size single-layer graphene device, with a gate electrode, which can modulate the transmission of terahertz and infrared waves. Using time-domain terahertz spectroscopy and Fourier-transform infrared spectroscopy in a wide frequency range (10-10000 cm^{-1}), we measured the dynamic conductivity change induced by electrical gating and thermal annealing. Both methods were able to effectively tune the Fermi energy, E_F, which in turn modified the Drude-like intraband absorption in the terahertz as well as the '2E_F onset' for interband absorption in the mid-infrared. These results not only provide fundamental insight into the electromagnetic response of Dirac fermions in graphene but also demonstrate the key functionalities of large-area graphene devices that are desired for components in terahertz and infrared optoelectronics.

cond-mat.mes-hall↗