基于压缩感知的空域可伸缩图像重构技术研究

In this research project, we focus on the spatially-scalable image reconstruction from the compressive sensing(CS)-sampled data of a natural scene. First, we will set up a new model that unifies the imaging process and the CS-sampling through the point reflectance function (PRF). Secondly, we will consider the spatially-scalable image reconstruction: (1) how to reconstruct low-resolution but high-quality images by using the CS data which are acquired from a natural scene at a low sampling rate so as to build up the downward scalability; and (2) how to construct high-resolution and high-quality images from the same CS data so as to build up the upward scalability (super-resolution). Thirdly, we will develop an adaptive CS-sampling framework that is based on some analysis of the reconstructed image at the receiver side so that multiple rounds of sampling-reconstruction can be supported. Finally, we will implement the image encryption based on the proposed spatially-scalable image reconstruction. Traditionally, the CS sampling is applied on the acquired image of a natural scene instead of the scene itself. To achieve the spatially-scalable reconstruction, an image of the same size (as the original one) needs to be reconstructed first; then, the spatial scalability is obtained via down-sampling or up-sampling. In this proposed research, we aim at unifying those three steps, including the imaging process, the CS sampling, and the spatially-scalable reconstruction, into a single one and promise to deliver a much better quality as compared to the traditional approaches.

本课题主要针对原始场景进行压缩感知采样并利用采样后的数据实现空域可伸缩的图像重构(包括向下的缩小重构和向上的扩展重构)。研究内容主要包括：(1)建立基于点反射函数的"成像-压缩感知"联合模型，从而将对原始场景的成像和压缩感知采样有机地结合起来；(2)利用经压缩感知采样后得到的样本，去构造高质量的低分辨率图像(缩小重构)或高分辨率图像(扩展重构)；(3)建立一种基于重构图像分析的自适应采样机理从而进行多次"采样-重构"；(4)实现空域可伸缩重构框架下的图像加密。在传统的基于压缩感知的图像处理中，人们完全忽略了成像的过程，仅仅是对已成像的图像进行压缩感知采样，在实现空域可伸缩图像重构时需要先进行和原图像等尺寸的重构，进而再进行下采样或者上采样（即缩小或扩展）。本课题所研究的方法，是为了实现成像、压缩感知采样和空域可伸缩重构的统一。在算法和重构图像的质量上，都将较传统方法有极大的改善和提高。

本课题在对原始图像场景进行压缩感知采样的基础上,进一步实现了对图像的缩小重构和扩展重构。研究内容主要包括：（1）通过建立基于点反射函数的“成像-压缩感知”联合模型，将对原始场景的成像和压缩感知采样有机地结合起来；（2）利用经压缩感知采样后得到的数据，构造高质量的低分辨率图像或高分辨率图像；（3）建立一种基于图像内部特征的自适应 “采样-重构”,提高压缩感知采样和重构效率。本课题对“成像-压缩感知”联合模型进行了研究，并以此为基础实现了基于压缩感知理论的空域可伸缩图像重构技术和自适应的“采样-重构”算法，实现了鲁棒性更强的加密算法。在低分辨率的图像重构方面，所提出的新型算法，在同样的采样率下，较传统算法峰值信噪比（PSNR）的提高可高达2dB；在自适应的“采样-重构”算法研究方面，所提出的新型算法，在同样的采样率下，较传统算法峰值信噪比（PSNR）的提高可高达3dB以上。本课题所研究的方法，是将成像、压缩感知采样和空域可伸缩重构融合为一体，在算法和重构图像的质量上，都将较传统方法有极大的改善和提高，对医学和军事等领域的应用都具有深远的的指导意义。相关结果发表SCI期刊论文7篇， EI会议论文9篇，申请发明专利3项。