It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the non-linear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation have, however, been restricted to Gaussian range kernels. In this work, we propose a novel approximation that can be applied to any range kernel, provided it has a pointwise-convergent Fourier series. More specifically, we propose to approximate the Gaussian range kernel of the bilateral filter using a Fourier basis, where the coefficients of the basis are obtained by solving a series of least-squares problems. The coefficients can be efficiently computed using a recursive form of the QR decomposition. By controlling the cardinality of the Fourier basis, we can obtain a good tradeoff between the run-time and the filtering accuracy. In particular, we are able to guarantee sub-pixel accuracy for the overall filtering, which is not provided by most existing methods for fast bilateral filtering. We present simulation results to demonstrate the speed and accuracy of the proposed algorithm.
The Hong Kong University of Science and Technology（香港科技大学）；University of Bristol（布里斯托大学）；Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）
Friedrich-Alexander Universität Erlangen-Nürnberg (FAU)（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；Siemens Healthcare GmbH（西门子医疗有限公司）
深度神经网络在低剂量CT去噪方面取得了巨大成功。然而，这些深度神经网络中的大多数都有几十万个可训练的参数。这与神经网络固有的非线性相结合，使得深度神经网络难以理解，责任心低。在这项研究中，我们介绍了JBFnet，神经网络的低剂量CT去噪。JBFnet的体系结构实现了迭代双边滤波。联合双边滤波器（JBF）的滤波器函数是通过浅层卷积网络学习的。引导图像由深度神经网络估计。JBFnet分为四个滤波块，每个滤波块执行联合双边滤波。每个JBF块由112个可训练的参数组成，使得噪声去除过程非常简单。在滤波之后添加噪声图（NM）以保留高级特征。我们用10名患者的身体扫描数据训练JBFnet，并在AAPM低剂量CT Grand Challenge数据集上对其进行测试。我们将JBFnet与最先进的深度学习网络进行比较。JBFnet在去除噪声的同时保留结构方面优于测试数据集上的CPCE 3D，GAN和深度GFnet。我们进行了几次消融研究，以测试我们的网络架构和训练方法的性能。我们目前的设置实现了最佳性能，同时仍然保持行为问责制。
A BEMD-Based Quaternion Filtering Approach Sharp-to-Soft Kernel CT Image Conversion
Sano Centre for Computational Medicine（萨诺计算医学中心）；AGH University of Krakow（AGH科技大学）；Jagiellonian University（雅盖隆大学）；Wroclaw University of Science and Technology（弗罗茨瓦夫理工大学）
Efficient Fourier Filtering Network with Contrastive Learning for AAV-based Unaligned Bimodal Salient Object Detection
Faculty of Robot Science and Engineering, Northeastern University（机器人科学与工程学院，东北大学）；College of Computing and Data Science, Nanyang Technological University（计算与数据科学学院，南洋理工大学）
Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations
College of Computer Science (College of Software), Inner Mongolia University（内蒙古大学计算机科学学院（软件学院））；Institute of Computational Imaging, Beijing Information Science and Technology University（北京信息科技大学计算成像研究所）；School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）
A Fractional Variational Approach to Spectral Filtering Using the Fourier Transform
Laboratory of Mathematical-Chemistry, Institute of Chemistry, Universidade Federal de Alfenas (UNIFAL)（数学化学实验室，化学学院，联邦阿尔费纳斯大学）；Institute of Exact Science, Universidade Federal de Alfenas (UNIFAL)（精确科学学院，联邦阿尔费纳斯大学）
