CIF: Small: Robust Sparse Recovery for Highly Correlated Data

CIF：小型：高度相关数据的稳健稀疏恢复

• 批准号: 1117545
• 负责人: Trac Tran
• 金额: $ 25万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1117545&HistoricalAwards=false
• 关键词: CIF; Small; Robust; Sparse; Recovery

Most natural signals are inherently sparse in certain bases or dictionaries where they can be approximately represented by only a few significant components carrying the most relevant information. In other words, the intrinsic signal information usually lies in a low-dimensional subspace and the semantic information is often encoded in the sparse representation. Processing of such signals in the sparsified domain is much faster, simpler, and more robust than doing so in the original domain, making sparsity an extremely powerful tool in many classical signal processing applications. Recently, with the emergence of the Compressed Sensing (CS) framework, sparse representation and related optimization problems involving sparsity as a prior called sparse recovery have increasingly attracted the interest of researchers in various diverse disciplines, from statistics, to information theory, applied mathematics, signal processing, coding theory and theoretical computer science.This research involves the analysis, development, and application of robust sparsity-driven algorithms for already-collected highly-correlated data sets where signals often exhibit a high level of joint-sparsity and rich correlation structure. Examples of such data include natural video sequences, volumetric medical images, huge image database, hyperspectral imagery (HSI), and raw synthetic aperture radar (SAR) signals. The research develops a novel unifying robust sparse-recovery framework based on context-aware and observable data-adaptive dictionaries,focusing on two classes of practical applications of sparse recovery: (i) Representative -- denoising, concealment, inpainting, enhancement; and (ii) Discriminative -- clustering, detection, classification, and recognition. Recovery/Discrimination accuracy is greatly improved by taking into account inter-patch spatial correlation, inter-frame temporal correlation, and by adapting algorithms dynamically based on local signal contents as well as by maximizing the level of discrimination within the sparse recovery process.

大多数自然信号在某些基础或字典中本质上是稀疏的，在这些基础或字典中，它们只能由携带最相关信息的几个重要组成部分来近似表示。换句话说，内在信号信息通常位于低维子空间中，而语义信息通常编码在稀疏表示中。在稀疏域中处理此类信号比在原始域中处理更快、更简单且更鲁棒，使得稀疏性成为许多经典信号处理应用中极其强大的工具。近年来，随着压缩感知（CS）框架的出现，稀疏表示和涉及稀疏性的相关优化问题（称为稀疏恢复）越来越吸引了各个不同学科的研究人员的兴趣，从统计学到信息论、应用数学、信号处理、编码理论和理论计算机科学。这项研究涉及对已收集的高度相关数据集进行稳健的稀疏性驱动算法的分析、开发和应用，其中信号通常表现出高水平的联合稀疏性和丰富的相关结构。此类数据的示例包括自然视频序列、立体医学图像、庞大的图像数据库、高光谱图像 (HSI) 和原始合成孔径雷达 (SAR) 信号。该研究开发了一种基于上下文感知和可观察数据自适应字典的新型统一鲁棒稀疏恢复框架，重点关注稀疏恢复的两类实际应用：（i）代表性的——去噪、隐藏、修复、增强； (ii) 判别性——聚类、检测、分类和识别。通过考虑块间空间相关性、帧间时间相关性、根据本地信号内容动态调整算法以及最大化稀疏恢复过程中的辨别水平，恢复/辨别精度得到极大提高。