CIF: Small: Robust Sparse Recovery for Highly Correlated Data

大多数自然信号在某些基或字典中是固有稀疏的，在这些基或字典中，它们可以由携带最相关信息的少数重要成分近似表示。换句话说，固有信号信息通常位于低维子空间中，而语义信息通常以稀疏表示进行编码。在稀疏化域中处理这种信号比在原始域中处理更快、更简单、更健壮，这使得稀疏性在许多经典信号处理应用中成为一种非常强大的工具。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）越来越引起了统计学、信息论、应用数学、信号处理、编码理论和理论计算机科学等各个学科研究者的兴趣。本研究涉及对已收集的高度相关数据集的鲁棒稀疏驱动算法的分析、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、体积医学图像、大型图像数据库、高光谱图像（HSI）和原始合成孔径雷达（SAR）信号。该研究基于上下文感知和可观察数据自适应字典开发了一种新颖的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——去噪、隐藏、修复、增强；（ii）判别——聚类、检测、分类和识别。通过考虑斑块间空间相关性、帧间时间相关性、基于局部信号内容动态调整算法以及在稀疏恢复过程中最大化识别水平，恢复/识别精度得到了极大的提高。

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.