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CIF: Small: Structured Signal Modeling via Nonconvex Optimization

CIF：小：通过非凸优化进行结构化信号建模

基本信息

批准号：
1527809
负责人：
John Wright
金额：
$ 49.98万
依托单位：
Columbia University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2015
资助国家：
美国
起止时间：
2015-08-01 至 2018-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1527809&HistoricalAwards=false
关键词：
CIF Small Structured Signal Modeling

项目摘要

Many problems in modern signal processing and data analysis can be cast as searching for a structured, low-dimensional model for observed data. Images, audio signals, video sequences, and more, can be modeled as sparse in an appropriate dictionary. Scientific data, from neural spike sorting to microscopy, can be modeled as superpositions of characteristic patterns, translated over space. Learned data representations yield excellent results on a variety of classical problems in image processing and vision, and are also play a crucial role in recent breakthroughs in signal classification and computational scientific discovery. In contrast, much less is known theoretically about the properties of learned representations, and of algorithms for learning them. This project develops theory and dedicated optimization algorithms, which are guaranteed, under appropriate conditions, to provide good representations for observed signals.The investigators study theoretical and computational aspects of a family of problems, including sparse dictionary learning, sparse deconvolution, and convolutional dictionary learning. The natural formulations of these problems are nonconvex. The goal of the project is to develop geometric insights into these nonconvex problems, and to use these insights to develop recovery theory and scalable, efficient algorithms. Key challenges include understanding the properties of local and global minima, and developing efficient algorithms that avoid stalling near saddle points. The algorithms are demonstrated on real signal data arising in image classification and scientific imaging.

现代信号处理和数据分析中的许多问题都可以归结为为观测数据寻找结构化的低维模型。图像、音频信号、视频序列等可以在适当的字典中建模为稀疏。科学数据，从神经尖峰分类到显微镜，可以建模为特征模式的叠加，在空间上转换。学习数据表示在图像处理和视觉领域的各种经典问题上取得了优异的成绩，并且在信号分类和计算科学发现的最新突破中也发挥了至关重要的作用。相比之下，从理论上讲，人们对学习表征的性质以及学习表征的算法知之甚少。本项目发展理论和专用优化算法，保证在适当条件下为观测信号提供良好的表示。研究人员研究了一系列问题的理论和计算方面，包括稀疏字典学习，稀疏反卷积和卷积字典学习。这些问题的自然形式是非凸的。该项目的目标是开发这些非凸问题的几何见解，并利用这些见解开发恢复理论和可扩展的高效算法。关键的挑战包括理解局部和全局最小值的特性，以及开发有效的算法来避免在鞍点附近失速。在图像分类和科学成像的实际信号数据上对算法进行了验证。