The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered backprojection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise tradeoff for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The U.S. Food and Drug Administration (FDA)-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This article focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models and data-driven methods based on machine learning techniques.

中文翻译：

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图像重建：从稀疏性到数据自适应方法和机器学习

医学图像重建领域大致有四种方法。第一类往往是分析方法，例如基于成像系统的简单数学模型的 X 射线计算机断层扫描 (CT) 的滤波反投影 (FBP) 和磁共振成像 (MRI) 的傅里叶逆变换。这些方法通常速度很快，但具有次优特性，例如 CT 的分辨率与噪声权衡较差。第二种类型是基于更完整的成像系统物理模型以及适当的传感器统计模型的迭代重建方法。这些迭代方法通过减少噪声和伪影来提高图像质量。其中美国食品和药物管理局 (FDA) 批准的方法基于相对简单的正则化模型。第三种方法旨在适应修改后的数据采集方法，例如减少 MRI 和 CT 中的采样以减少扫描时间或辐射剂量。这些方法通常涉及涉及稀疏性或低秩等假设的数学图像模型。第四种方法用受机器学习领域启发的数据驱动或自适应模型取代信号和系统的数学设计模型。本文重点关注医学图像重建的两个最新趋势：基于稀疏或低秩模型的方法和基于机器学习技术的数据驱动方法。