学习现有但未知的反向映射的稳定近似:应用到半时循环拉登变换
Refik Mert Cam1, Umberto Villa2, Mark A Anastasio1,3
1Department of Electrical and Computer Engineering, University of Illinois Urbana-Champaign, Urbana, IL 61801, United States of America.
Inverse problems
|June 27, 2024
概括
监督深度学习通过学习现有分析解决方案问题的稳定反向映射来改善图像重建. 这种方法显示了强度和通用性,用于像光声学计算机断层扫描这样的应用.
科学领域:
- 医疗成像医学成像
- 计算成像技术的成像
- 应用数学 应用数学 应用数学
背景情况:
- 监督深度学习 (DL) 为图像重建提供了隐含的规范化,但在不好的问题中面临着强度问题.
- 现有的DL方法在解决缺乏独特,稳定的反向映射的问题时,与不稳定性作斗争.
- 探索DL的新应用程序用于图像重建问题,其中存在一个稳定的,尽管未知,反向映射.
研究的目的:
- 在已知稳定反向映射的场景中调查监督DL的图像重建性能.
- 开发一个基于DL的方法来近似一个未知的反向映射,以提高概括性.
- 探索DL的潜力,揭示未知的分析反式的洞察力.
主要方法:
- 使用卷积神经网络 (CNN) 开发了一种学习过的反向投影方法.
- 美国有线电视新闻网 (CNN) 从辐射截断的圆形转换 (CRT) 数据对图像重建中的未知过操作进行了近似计算.
- 该方法是专门为"半时"测量数据设计的.
主要成果:
- 开发的学习过反向投影方法表现出稳定的性能.
- 该方法表现出强大的概括能力,在与训练集明显不同的数据上表现良好.
- DL方法成功地近似了反向映射,而不需要基于优化的重建.
结论:
- 监督深度学习可以有效地学习已知的稳定解决方案的图像重建问题的稳定反向映射.
- 开发的基于CNN的方法为特定的反向问题提供了稳定和可泛化的替代方案.
- 这种方法对基于波的成像方式具有前景,包括光声学计算机断层扫描.
相关概念视频
01:20Inverse z-Transform by Partial Fraction Expansion
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The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
To begin the process, the poles of the function are identified and the function is...
317
01:21Linear Approximation in Time Domain
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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01:26Linear Approximation in Frequency Domain
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
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01:10Reconstruction of Signal using Interpolation
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Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
191
01:17Region of Convergence
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The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...
409
01:24Properties of DTFT II
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In the study of discrete-time signal processing, understanding the properties of the Discrete-Time Fourier Transform (DTFT) is crucial for analyzing and manipulating signals in the frequency domain. Several properties, including frequency differentiation, convolution, accumulation, and Parseval's relation, offer powerful tools for signal analysis.
The frequency differentiation property is illustrated by considering a DTFT pair and differentiating both sides with respect to ω.
The frequency differentiation property is illustrated by considering a DTFT pair and differentiating both sides with respect to ω.
191