Rousseau Sylvain, Helbert David
IEEE Trans Image Process. 2019 Jul 17. doi: 10.1109/TIP.2019.2927334.
One key issue in compressive sensing is to design a sensing matrix that is random enough to have a good signal reconstruction quality and that also enjoys some desirable properties such that orthogonality or being circulant. The classic method to construct such sensing matrices is to first generate a full orthogonal circulant matrix and then select only a few rows. In this paper, we propose a refined construction of orthogonal circulant sensing matrices that generates a circulant matrix where only a given subset of its rows are orthogonal. That way, the generation method is a lot less constrained leading to better sensing matrices and we still have the desired properties. The proposed partial shift-orthogonal sensing matrix is compared to random and learned sensing matrices in the frame of signal reconstruction. This sensing matrix is pattern-dependent and thus efficient to detect color patterns and edges from the measurements of a color image.
压缩感知中的一个关键问题是设计一个足够随机的感知矩阵，以具备良好的信号重构质量，并且还具有一些理想特性，如正交性或循环性。构建此类感知矩阵的经典方法是首先生成一个完整的正交循环矩阵，然后仅选择其中的少数几行。在本文中，我们提出了一种正交循环感知矩阵的优化构造方法，该方法生成的循环矩阵中只有给定的行子集是正交的。通过这种方式，生成方法的约束大大减少，从而得到更好的感知矩阵，同时我们仍然具备所需的特性。在信号重构框架下，将所提出的部分移位正交感知矩阵与随机感知矩阵和学习型感知矩阵进行了比较。这种感知矩阵与模式相关，因此能有效地从彩色图像的测量中检测颜色模式和边缘。
