Computing a projection operator onto the null space of a linear imaging operator: tutorial.
Computing a projection operator onto the null space of a linear imaging operator: tutorial.
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DOI：
10.1364/josaa.443443
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发表时间：
2022-03-01
期刊：
影响因子：
--
通讯作者：
中科院分区：
文献类型：
--
作者：
许多成像系统可以用线性算子来近似描述，线性算子将物体属性映射到离散测量值的集合。然而，即使在没有测量噪声的情况下，这些操作人员通常对物体的某些成分是“盲目的”，因此在成像过程中存在信息丢失。在数学上，这可以用成像算子可以拥有零空间这一事实来解释。根据定义，零空间中的所有对象都映射到相同的零测量值集合，因此对成像系统是不可见的。因此，在比较和/或设计成像系统时，表征成像算子的零空间是至关重要的。零空间的表征也有助于图像重建方法的正则化策略的设计。通常，通过相关的投影算子来表征零空间是一项计算要求很高的任务。在本教程中，计算程序建立投影算子，映射一个对象到一个离散到离散成像算子的零空间进行了调查。本文还提出了一种采用线性自编码器的基于机器学习的方法。以生物医学成像为例，对其计算复杂度和存储需求进行了比较。
Many imaging systems can be approximately described by a linear operator that maps an object property to a collection of discrete measurements. However, even in the absence of measurement noise, such operators are generally “blind” to certain components of the object and hence there is information lost in the imaging process. Mathematically, this is explained by the fact that the imaging operator can possess a null space. All objects in the null space, by definition, are mapped to a collection of identically zero measurements and are hence invisible to the imaging system. As such, characterizing the null space of an imaging operator is of fundamental importance when comparing and/or designing imaging systems. A characterization of the null space can also facilitate the design of regularization strategies for image reconstruction methods. Characterizing the null space via an associated projection operator is, in general, a computationally demanding task. In this tutorial, computational procedures for establishing projection operators that map an object to the null space of a discrete-to-discrete imaging operator are surveyed. A new machine learning-based approach that employs a linear autoencoder is also presented. The procedures are demonstrated by use of biomedical imaging examples and their computational complexities and memory requirements are compared.
影响因子：
3.5
作者：
Zeng GL;Gullberg GT
通讯作者：
Gullberg GT