CIF: Small: Theory and Algorithms for Scalable Learning of Sparse Representations

CIF：小：稀疏表示的可扩展学习的理论和算法

• 批准号: 1320953
• 负责人: Yoram Bresler
• 金额: $ 49.97万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1320953&HistoricalAwards=false
• 关键词: CIF; Small; Theory; Algorithms; Scalable

Many applications in signal and image processing and imaging depend critically on sparse representations for natural signals or images. This research addresses the development of improved sparse representations that are directly adapted to the data, rather than being fixed a priori by general theoretical considerations. Such data-driven learning of sparse structure has been finding broad applications. The improvements over fixed representation are especially significant for high-dimensional data. This research aims to overcome limitations of the current methods by reducing the computation to enable scaling to big data problems, improving robustness and predictability of outcome, and developing a theory quantifying the expected performance and the factors affecting it. Applications are foreseen in all areas of science and engineering, including medical diagnostics, multimedia, defense, manufacturing, communications, database retrieval, and data analytics. In particular, this research leverages a new formulation recently introduced by the PI for data-driven learning of "sparsifying transforms", which are relatives of analysis dictionaries. Initial results in image denoising show slightly better PSNR than with learnt synthesis dictionaries, but at orders of magnitude less computation. Theory predicts better scaling with exemplar size, and experiments demonstrate robust convergence irrespective of initialization. Specific objectives of this research are: (1) develop theory and scalable algorithms for learning sparsifying transforms; (2) develop theory for joint learning of sparsifying transforms and signal recovery in compressed sensing and other inverse problems; and, (3) demonstrate key large-scale applications with real data. These applications include: (i) denoising, restoration, and compressed sensing of 3D and 4D data in magnetic resonance imaging, in computerized tomography, in microscopy, and in video; and (ii) image classification and recognition.

信号和图像处理以及成像中的许多应用严重依赖于自然信号或图像的稀疏表示。这项研究解决了改进的稀疏表示，直接适应数据的发展，而不是固定的先验一般理论的考虑。这种稀疏结构的数据驱动学习已经得到了广泛的应用。相对于固定表示的改进对于高维数据尤其重要。该研究旨在通过减少计算量来克服当前方法的局限性，从而能够扩展到大数据问题，提高结果的鲁棒性和可预测性，并开发量化预期性能及其影响因素的理论。预计在科学和工程的所有领域，包括医疗诊断，多媒体，国防，制造，通信，数据库检索和数据分析。 特别是，这项研究利用了PI最近推出的一种新配方，用于数据驱动的“稀疏化变换”学习，这是分析字典的亲戚。图像去噪的初步结果显示，PSNR略好于学习的合成字典，但在数量级更少的计算。 理论预测更好的缩放与样本的大小，实验证明了鲁棒的收敛，无论初始化。 本研究的具体目标是：（1）开发理论和可扩展的算法学习稀疏化变换;（2）开发理论的联合学习稀疏化变换和信号恢复在压缩感知和其他逆问题;和（3）展示关键的大规模应用与真实的数据。这些应用包括：（i）磁共振成像、计算机断层扫描、显微镜和视频中3D和4D数据的去噪、恢复和压缩感测;以及（ii）图像分类和识别。