Compressive Color Pattern Detection Using Partial Orthogonal Circulant Sensing Matrix

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.