基于稀疏优化与低秩逼近及非局部化方法的红外图像超分辨率重建研究

Super resolution is considered as one of the “holy grails” for improving image quality. By using super resolution reconstruction to improve resolution of infrared image and recover the degraded image accurately without increasing the system complexity. Based on sparse optimization, low-rank approximation and non-local approach, the item mainly studies sparse representational models and related efficient algorithms for super resolution reconstruction of infrared image. We focus on mathematical theories and methods via sparse representation to implement super resolution of infrared image accurately. Study the form of infrared images for target ,object and noise feature under the frame of sparse representation and low-rank approximation, and establish sparse optimization ,low-rank approximation and non-local approach models which can reflect the mentioned features exactly. Design efficient and numerical stability algorithms for solving the above models. The aims of the item are to refine and expand theories and methods for spares optimization, low-rank approximation and non-local approach with their applications to improve speed and quality of super resolution reconstruction for infrared image. The related results of the item has theoretical significance and application value in military and scientific research.

图像超分辨率被认为是提高图像质量的“圣杯”之一。通过超分辨率重建方法来提高红外图像的分辨率，其目的是在不增加系统复杂性的前提下使退化的图像尽可能恢复到原来的真实面貌。本项目基于稀疏优化、低秩逼近与非局部化方法研究红外图像超分辨率重建的稀疏表示模型及其高效算法。重点研究红外图像稀疏表示准确实现超分辨率重建的数学理论与方法，红外图像的目标特征、背景特征与噪声特征等在稀疏表示与低秩逼近框架下变换域的表现形式及规律，建立能综合体现红外图像各特征的稀疏优化与低秩逼近模型以及非局部化方法模型；根据建立的相关模型，设计相应的高效数值稳定的求解方法。本项目的研究进一步完善和拓展稀疏优化与低秩逼近及非局部化方法在提高红外图像超分辨率重建处理的质量及速度方面的应用，具有重要的理论意义与科研、军事应用价值。

本课题立足于现在及未来几年国内红外图像及成像硬件技术水平，以先进的基于数据驱动的非局部稀疏表示框架的超分辨率重建方法为出发点，借鉴近年发展起来的稀疏优化、非局部等相关理论，研究建立了基于非局部稀疏变换与矩阵低秩逼近的超分辨率重建模型，并设计相应的数值稳定快速求解算法。重点研究了自适应非局部稀疏变换框架的构造、建模以及高效算法设计中的若干理论和关键技术。项目的研究一方面可完善和拓展自适应非局部稀疏表示框架方法本身的理论、技术和算法，另一方面将研究成果应用于我国实测红外图像成像处理，实现红外图像的高分辨率重建，以使我国已获取的大量红外图像数据发挥更大的应用价值。