Valiev Institute of Physics and Technology of Russian Academy of Sciences, Moscow 117218, Russia.
Sensors (Basel). 2023 Jan 21;23(3):1247. doi: 10.3390/s23031247.
This article proposes the application of a new mathematical model of for solving inverse problems using a learning method, which is similar to using deep learning. In general, the spots represent vague figures in abstract "information spaces" or crisp figures with a lack of information about their shapes. However, crisp figures are regarded as a special and limiting case of spots. A basic mathematical apparatus, based on L4 numbers, has been developed for the representation and processing of qualitative information of elementary spatial relations between spots. Moreover, we defined L4 vectors, L4 matrices, and mathematical operations on them. The developed apparatus can be used in Artificial Intelligence, in particular, for knowledge representation and for modeling qualitative reasoning and learning. Another application area is the solution of inverse problems by learning. For example, this can be applied to image reconstruction using ultrasound, X-ray, magnetic resonance, or radar scan data. The introduced apparatus was verified by solving problems of reconstruction of images, utilizing only qualitative data of its elementary relations with some scanning figures. This article also demonstrates the application of a spot-based inverse Radon algorithm for binary image reconstruction. In both cases, the spot-based algorithms have demonstrated an effective denoising property.
本文提出了一种新的数学模型，用于通过学习方法解决逆问题，该方法类似于使用深度学习。一般来说，点表示抽象“信息空间”中的模糊图形或具有其形状信息缺失的清晰图形。然而，清晰图形被视为点的特殊和限制情况。已经开发了一个基于 L4 数的基本数学工具，用于表示和处理点之间基本空间关系的定性信息。此外，我们定义了 L4 向量、L4 矩阵及其在它们上的运算。该开发的仪器可用于人工智能，特别是用于知识表示和建模定性推理和学习。另一个应用领域是通过学习解决逆问题。例如，这可应用于使用超声、X 射线、磁共振或雷达扫描数据进行图像重建。所引入的仪器通过仅利用与其某些扫描图形的基本关系的定性数据来解决图像重建问题进行了验证。本文还展示了基于点的逆 Radon 算法在二进制图像重建中的应用。在这两种情况下，基于点的算法都表现出了有效的去噪特性。
