Learning Geometry for Inverse Problems in Imaging

学习成像反问题的几何

• 批准号: 1821342
• 负责人: Jeffrey Jackson
• 金额: $ 10万
• 依托单位: Duquesne University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1821342&HistoricalAwards=false
• 关键词: Learning; Geometry; Inverse; Problems; Imaging

The quantity of digital image data our society relies on for medical, military, and a wide range of engineering and scientific applications continues to increase, yet digital images still typically exhibit some level of degradation during formation, transmission, and storage, often obscuring vital information. Despite significant advances in the fields of image processing and computer vision, this problem still persists due to the difficulty in accurately modeling random degradations such as noise, pixel loss, and blur. The main objectives for this project are to learn critical geometric and higher order image features for accurately solving a variety of inverse problems in imaging, including image denoising, image deblurring, image inpainting (filling in of missing data), and super-resolution. The new algorithms developed in this project are expected to yield improvements over existing algorithms in the form of standard image quality metrics as well as in the preservation of accurate, fine details, a feature missing from many current state of the art image processing algorithms, yet vital for automatically interpreting this image data in practice. In recent work the PI and collaborators have developed several frameworks for image denoising that attempt to recover an image from a denoised geometric feature of the image. These approaches have successfully improved upon existing state of the art denoising algorithms, providing information in the reconstruction that has been elusive using alternate approaches. The challenge in working with this geometric data is that while it is very robust in practice, mathematically sound mechanisms developed for handling natural image data do not necessarily apply to their geometric features. This project involves learning geometric descriptors from image data that have suffered from some combination of the aforementioned random and/or linear degradations for the purpose of aiding in image reconstruction, analysis, and interpretation. Preliminary analyses and experiments indicate that the benefits of this approach could be significant, yet computationally intensive experiments are required to explore how best to exploit these benefits in practice. Theoretical analyses of these models will be an important part of this project as well, in order to better to understand when these models are guaranteed to be reliable in practice.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

我们的社会对医疗、军事以及广泛的工程和科学应用所依赖的数字图像数据量持续增加，但数字图像在形成、传输和存储过程中通常仍然表现出一定程度的退化，往往会掩盖重要信息。尽管图像处理和计算机视觉领域取得了重大进展，但由于难以准确地对噪声、像素丢失和模糊等随机退化进行建模，该问题仍然存在。该项目的主要目标是学习关键的几何和高阶图像特征，以准确解决成像中的各种逆问题，包括图像去噪、图像去模糊、图像修复(填补缺失数据)和超分辨率。在这个项目中开发的新算法有望以标准图像质量度量的形式产生对现有算法的改进，以及在保存准确、精细的细节方面，这是许多当前最先进的图像处理算法所缺少的特征，但对于在实践中自动解释这些图像数据至关重要。在最近的工作中，PI和合作者开发了几个图像去噪框架，试图从图像的去噪几何特征中恢复图像。这些方法成功地改进了现有的最先进的去噪算法，在使用替代方法的重建中提供了难以捉摸的信息。处理这些几何数据的挑战在于，尽管它在实践中非常健壮，但为处理自然图像数据而开发的数学上合理的机制并不一定适用于它们的几何特征。该项目涉及从遭受上述随机和/或线性退化的某种组合的图像数据中学习几何描述符，以帮助图像重建、分析和解释。初步分析和实验表明，这种方法的好处可能是显著的，但需要计算密集的实验来探索如何最好地在实践中利用这些好处。对这些模型的理论分析也将是该项目的重要部分，以便更好地理解这些模型何时被保证在实践中是可靠的。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Learned Regularizers and Geometry for Image Denoising

• 发表时间: 2021
• 作者: Stacey Levine;Ryan M Cecil;M. Bertalmío

Quantifying Iron Overload using MRI, Active Contours, and Convolutional Neural Networks

使用 MRI、主动轮廓和卷积神经网络量化铁过载

• 发表时间: 2019
• 期刊: Duquesne University
• 作者: Sajewski, Andrea and

Pointwise Besov Space Smoothing of Images

图像的逐点贝索夫空间平滑

• DOI: 10.1007/s10851-018-0821-1
• 发表时间: 2019
• 期刊: Journal of Mathematical Imaging and Vision
• 影响因子: 2
• 作者: Buzzard, Gregery T.;Chambolle, Antonin;Cohen, Jonathan D.;Levine, Stacey E.;Lucier, Bradley J.
• 通讯作者: Lucier, Bradley J.