CAREER: Signal Recovery from Generative Priors

人工智能和机器学习的最新进展使人们在理解数字图像中的对象的任务中表现出色。 这些发展使一类新的算法，磁共振成像，天文成像，显微镜和成像的基础上X射线衍射。 这些新算法有可能大大减少用于成像目的的科学和医学数据收集的时间和费用。 例如，使用这些技术，MRI机器可以提高效率，允许更短的扫描时间和更短的医疗等待。 此外，这些新技术可以通过最小化分子成像的成本来加速药物发现和开发的过程。 虽然最近出现了一些新的算法，但目前对它们的理论理解很少。 这是一个严重的问题，因为专业人员进行科学发现和医学诊断所依赖的技术在常见和新的情况下应该是可靠的。 研究人员和他的同事们介绍了用于恢复图像的新方法，科学和医学，成功的同时需要比以前的方法更少的数据。 此外，研究人员和他的同事还为为什么这种成像方法可以恢复足够高质量的图像提供了数学依据。 研究生正在从事该项目的研究，研究员和他的同事们在生成神经网络先验的背景下，针对多信号恢复问题发展了严格的恢复理论。 这些问题是线性压缩传感，相位恢复和盲反卷积。 在每一个中，恢复问题被描述为在所需信号属于由人工神经网络给出的预训练生成模型的范围的约束下的非凸优化。 对于每个问题，研究者和他的同事提供了（1）计算效率高，具有收敛保证的特定数值算法，（2）相对于自然信号建模流形的维度，以最佳样本复杂度运行，（3）适用于现实的神经网络架构。 这项工作的影响来自两个想法：（1）在许多情况下，从数据中学习的生成先验可以提供比稀疏先验更低维的表示;（2）在相位检索等非线性逆问题中，生成先验可能比稀疏先验更容易利用。 该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Recent progress in artificial intelligence and machine learning has led to exceptional performance in tasks involving understanding what objects are in digital images. These developments enable a new class of algorithms for Magnetic Resonance Imaging, astronomical imaging, microscopy, and imaging based on X-ray diffractions. These new algorithms have the potential to drastically reduce the time and expense of scientific and medical data collection for the purpose of imaging. For example, using these techniques, MRI machines could increase in efficiency, allowing shorter scan times and shorter waits for medical care. Additionally, these new techniques can accelerate the process of drug discovery and development by minimizing the cost of imaging of molecules. While some new algorithms have recently appeared, theoretical understanding of them is currently minimal. This is a serious concern as technology, upon which professionals make scientific discoveries and medical diagnoses, should be reliable in common and novel situations. The investigator and his colleagues introduce novel approaches for recovering images, scientific and medical, that succeed while needing less data than earlier methods. Additionally, the investigator and his colleagues provide mathematical justification for why such imaging methods recover a sufficiently high-quality image. Graduate students are engaged in the research of the project.The investigator and his colleagues develop a rigorous recovery theory for multiple signal recovery problems in the context of generative neural network priors. These problems are linear compressed sensing, phase retrieval, and blind deconvolution. In each, the recovery problem is phrased as a nonconvex optimization under the constraint that the desired signal belongs to the range of a pre-trained generative model given by an artificial neural network. For each problem, the investigator and his colleagues provide (1) computationally efficient, specific numerical algorithms with convergence guarantees that (2) operate at optimal sample complexity with respect to the dimensionality of the modeled manifold of natural signals, and (3) apply to realistic neural network architectures. The impact of this work follows from two ideas: (1) generative priors learned from data may provide lower-dimensional representations than sparsity priors in many contexts; and (2) generative priors may be easier to exploit than sparsity priors in nonlinear inverse problems such as phase retrieval. Graduate students are engaged in the research of the project.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.