图像压缩感知重建方法研究

This research focuses on the nonlocal low rank prior knowledge based image compressive sensing reconstruction method. We analyze the key issues that affect the algorithm performance and the weak links of the algorithm applied to the actual situations. We make full use of the theory of blind compressive sensing and robust compressive sensing, research results in matrix completion field and the idea of multiprior fusion to do research..In the reconstruction aspect of low-rank data, almost all the image CS methods ignores the relationship between pixels because it deals with the vector form of image patches. We propose a compressive sensing reconstruction method based on low-rank tensor regularization, which can simultaneously regularize low-rank property and preserve the structural information of the image, to enhance the performance of the algorithm..In the solution aspect of rank regularization model, how to solve the resulting rank regularization problem which is known as an NP-hard problem is critical to the recovery results. We propose a compressive sensing reconstruction method based on truncated weighted schatten-p norm to accurately exploit nonlocal low-rank property and improve the quality of the reconstructed image..In dealing with noise problem, current CS approaches rarely take noise into consideration or only consider the noise generated in the process of transmission. We do research on the robust compressive sensing reconstruction method based on the m-estimator theory which is used to improve the robustness to noise..Drawing on the idea of multiprior fusion methods, we propose an image compressive sensing reconstruction method based on local and nonlocal priors to further improve the quality of image reconstruction.

本课题围绕基于非局部低秩先验的图像压缩感知重建算法，重点分析了影响算法性能的关键问题以及算法应用于实际的薄弱环节，充分利用盲压缩感知理论、鲁棒压缩感知理论、矩阵填充领域的研究成果和多先验知识融合的思想展开研究： .低秩数据的构造方面，几乎所有的方法将图像块拉成向量，忽略了像素点间的联系，提出基于低秩张量约束的重建方法，同时挖掘低秩性和保持图像的结构信息，提高算法的性能。.在秩正则化优化模型的求解方面，分析秩正则化问题的求解结果直接决定着重建质量，提出基于截断加权schatten-p范数的重建方法，准确挖掘低秩性，提高图像的重建质量。.在噪声问题的处理方面，当前的压缩感知方法很少考虑噪声或仅考虑传输过程中产生的噪声，研究基于m-估计理论的鲁棒重建方法，提高对噪声的抗干扰性。.借鉴多先验融合方法的思想，提出基于局部和非局部先验的重建方法，进一步提升图像重建质量。

压缩感知突破了传统的奈奎斯特采样定理的限制，使得信号精确重建必需的采样率不再取决于信号的带宽，而取决于更能反映信号本质的稀疏度。压缩感知理论的突破性发展，其在图像处理、生物物理、计算科学等多学科领域的潜在应用价值，引起了越来越多的学者的关注。压缩感知重建算法作为压缩感知理论的核心问题，直接决定了压缩感知理论在各领域实际应用的成败，因此对于它的研究具有重要的意义。.本课题围绕基于非局部低秩先验知识的图像压缩感知算法，重点分析了影响算法性能的关键问题以及算法应用于实际的薄弱环节，充分利用盲压缩感知理论、鲁棒压缩感知理论、矩阵填充领域的研究成果和多先验知识融合的思想展开研究。在秩正则化优化模型的求解方面，提出了基于截断加权schatten-p范数的压缩感知重建方法；在噪声问题的处理方面，提出了基于非凸m-估计理论的鲁棒压缩感知重建方法；借鉴多先验融合方法的思想，提出了基于稀疏和非局部低秩先验的图像盲压缩感知重建方法和基于同时稀疏和低秩先验的多通道脑电波信号重建方法。另外，将相关理论和方法推广应用于交通车辆轨迹预测、人脸识别等领域，取得了前期性探索性研究成果。.在项目的支持下，项目组合计发表论文7篇，其中国际期刊5篇，国内核心期刊2篇，SCI收录5篇，申请发明专利1项，授权实用新型专利2项。.该项目的研究将在图像和信号处理方面具有广阔的应用前景，同时对于推动图像复原和模式识别的发展具有重要的理论意义和应用价值。