Non-convex Variational Image Processing: Boosting Classical Methods with Machine Learning

机器学习和人工智能的最新进展，特别是基于人工神经网络的进展，使我们能够建立系统，以类似人类的精度解决困难的信息处理问题。例如，神经网络可以识别物体，预测蛋白质如何折叠，自动化制造过程，并使用计算机视觉来导航车辆或分析卫星图像。不幸的是，这些先进的人工智能系统都有自己独特的问题。像人类一样，神经网络的行为也会不规律，有时当被要求执行与训练稍有不同的任务时，神经网络会做出奇怪和无法解释的决定。因此，当需要可靠性、可解释性和计算速度时，经典的图像和信号处理方法仍然是首选的解决方案。本研究项目的目标是将神经网络的性能和能力与速度、可靠性和经典算法相结合。本研究亦设有研究生与本科生实习生的综合教学计划。为了实现这一目标，我们考虑了三个相互关联的研究重点。首先，我们考虑深度网络可以帮助自动化和改进经典算法的方法。例如，网络可用于自动选择超参数，选择目标函数以最小化，识别数据中存在的噪声类型和水平，并做出优化传统成像系统性能所需的其他决策。其次，我们考虑将神经网络“插入”到经典变分成像方法中的方法。例如，经典的图像先验（如小波稀疏性或总变分）可以被神经网络定义的更复杂的先验所取代。第三，我们考虑了当复杂神经网络被用作经典优化问题的组成部分时出现的最小化问题的有效算法。更好的算法将使我们能够在没有人为监督的情况下有效地解决这些复杂的问题。这一套新的方法有可能提高PI研究过的一系列重要实际问题的技术水平。这包括增强用于新材料显微镜的去模糊问题，增强用于识别半导体制造故障的分割算法，以及解决用于医疗应用的复杂资源分配问题。该奖项反映了美国国家科学基金会的法定使命，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 advances in machine learning and AI, particularly those based on artificial neural networks, have enabled us to build systems that solve difficult information processing problems with human-like accuracy. For example, neural networks can recognize objects, predict how proteins fold, automate manufacturing processing, and use computer vision to navigate a vehicle or analyze satellite imagery. Unfortunately, these advanced AI systems come with their own unique problems. Like humans, neural networks can behave erratically, sometimes making strange and unexplainable decisions when asked to perform tasks that differ even a little from their training. For this reason, classifical image and signal processing methods are still the go-to solution when reliability, interpretability, and computational speed at needed. The goal of this research project is to mash up the performance and power of neural networks with the speed and reliability and classical algorithms. This research project also features an integrated teaching plan involving graduate students and undergraduate interns. To achieve this goal, we consider three interrelated research thrusts. First, we consider ways that deep networks can help to automate and improve classical algorithms. For example, networks can be used to automate the selection of hyper-parameters, choose objective functions to minimize, identify noise types and levels that are present in data, and make other decisions that are needed to optimally tune the performance of classical imaging system. Second, we consider ways that neural networks can be 'plugged in' to classical variational imaging methods. For example, classical image priors (such as wavelet sparsity or total variation), can be replaced with more sophisticated priors defined by neural networks. Third, we consider efficient algorithms for solving minimization problems that arise when complex neural networks are used as components in classical optimization problems. Better algorithms will allow us to solve these complex problems efficiently, and without human oversight. This new suite of approaches has the potential to improve that state of the art for a range of important practical problems that have been studied by the PI. This includes enhancing deblurring problems of the type used for microscopy of new materials, boosting segmentation algorithms used to identify faults in semiconductor manufacturing, and solving complex resource allocation problems for medical applications.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.