隐空间稀疏与结构化先验下的非线性压缩感知研究

One of the conditions of realizing compressed sensing is the sparsity (or compressibility) of observation objects under an explicit linear model. However, the observation objects in real physical environment always have the characteristics of high dimensionality, variability, complexity and so on, which makes the sparsity difficult to be satisfied. Consequently it will result in high-cost measurement and low-quality information reconstruction of objects. It is well known that the representation of high-dimensional information universally has the latent sparsity and structure. This project is aimed at high dimensional information acquisition and reconstruction in complicated scene, based on the nonlinear sparse encoding mechanism of biological vision. Further more, this project plans to explore the novel theories and methods for remote sensing information acquisition and reconstruction, based on nonlinear compressed sensing. Including: 1) The mathematical model establishing of the nonlinear latent sparse representation and nonlinear compressed sensing, based on the reproducing kernel structure and statistical learning theory; 2) The analysis of the structural prior of observation objects, the design of the structural observation waveform and multi-channel information sampling scheme, the implementation of reconfigurable optimized sampling based on autonomous attention mechanism; 3) The study of linear reconstruction methods of nonlinear sparse representation, and the development of fast non-iterative information restoration algorithm; 4) The construction of compressed information acquisition and reconstruction prototype system for remote sensing scene based on nonlinear compressed sensing. It is expected to achieve the low-cost and high-accuracy information acquisition and reconstruction under complex remote sensing scenes based on the above research. Our works hope to explore more efficient compressed sensing schemes for the practical application of compressed sensing technology.

压缩感知实现的条件之一是观测对象在显式线性模型下的稀疏性(或可压缩性)，然而实际物理环境中的对象通常具有高维、变化与复杂等特点，使得这一条件难以严格满足，导致高代价观测与低质量重建。潜在的稀疏性与结构性是高维信息表示的普遍属性，课题针对复杂场景下的高维信息获取与重建，借鉴生物视觉的非线性稀疏编码机制，探索基于非线性压缩感知的遥感信息获取与重建的新理论与方法。具体包括：1)基于再生核构造与统计学习理论，建立隐空间稀疏下的非线性稀疏表征与压缩感知的数学模型；2)分析观测对象的结构化先验，设计结构化的观测波形与多通道信息采样方案，实现自主注意下的可重配置优化采样；3)研究非线性稀疏表征下的线性重建方法，发展快速非迭代信息复原算法；4)建立基于非线性压缩感知的遥感场景压缩信息采集与重建的验证系统。期望通过上述研究，实现低成本、高精度的遥感信息压缩获取与重建，为压缩感知工程化探索更加有效的方案。

潜在的稀疏性与结构性是高维信息表示的普遍属性，项目针对复杂场景下的遥感观测对象，将传统压缩感知的线性稀疏假设拓展至非线性假设，挖掘并建模隐空间中的稀疏性与结构性，探索隐空间稀疏与结构化先验下的非线性压缩感知理论与实现。主要具体内容：1)建立隐空间稀疏下的非线性稀疏表征与压缩感知的数学模型；2)设计结构化的观测波形与多通道信息采样方案，实现自主注意下的可重配置优化采样；3)研究非线性稀疏表征下的线性重建方法，发展快速非迭代信息复原算法；4)建立基于非线性压缩感知的遥感场景压缩信息采集与重建的验证系统。.项目围绕信息稀疏表征、获取与重建，依序完成了各项计划内容。第一，分析了高维遥感数据中富含的多种未知结构，系统研究了遥感数据几何结构稀疏与张量结构稀疏性的描述与度量，提出了一系列复杂影像的稀疏结构学习方法(几何结构稀疏表征、稀疏张量字典学习、稀疏张量深度神经网络等)，从数据中自动学习隐空间中的未知结构，在多组遥感影像数据上相比线性方法稀疏度提高平均超9%；第二，面向航天/空侦察中的高维光学与雷达目标信息，设计了一种非线性张量光谱压缩成像方法，以及一种非线性压缩感知SAR目标成像方法，显著提升了10%采样率及之下的压缩成像质量，解决了传统压缩感知方法在低采样率下性能恶化的问题；第三，探索了基于深度学习的非线性压缩感知的可行性，针对深度学习受限于大量训练数据的局限，提出基于元学习的非线性压缩SAR成像方法。设计了大倍率压缩和细节保持的深度学习网络模型，提升在低采样率下的影像复原质量。最后，项目组成员搭建了器由雷达、热红外摄像头、光学摄像头等构成的数据采集平台，验证非线性压缩感知理论与方法的可行性。通过上述研究，拓展并结合了机器学习和压缩感知领域的研究，促进领域间交叉融合；提升了低成本采样下目标信息获取的精度，解决了压缩感知实用中重构条件难以严格满足的难题，为稀疏采样工程化探索了更加适用可行的理论与技术方案。