Analysis of measurement matrices for a single-pixel-camera based on both theoretical and practical performance

Compressed Sensing provides an innovative imaging technique with fundamental differences to conventional imaging. A collection of low-resolution measurements is taken to reconstruct a picture with higher resolution computationally. The significant advantage is the small number of measurements and reduced number of measured pixels compared to the number of pixels in the reconstructed picture. This can be achieved because of sparsity. A realization of this concept is the single-pixel-camera, which uses a single-pixel-detector to measure only the brightness of the target scene after modulation with a digital micromirror device. Obviously, the patterns used for the modulation must satisfy certain properties. For example, the coherence of the measurement matrix containing those patterns is related to the performance of the camera. It seems efficient to construct matrices with optimal coherence or other performance parameters. Other approaches use specialized matrices depending on specific applications. This paper discusses the relation between the mathematical properties such as coherence and other parameters and the practical results from exemplary tests. Therefore matrices from different approaches are implemented and combined with a primal-dual-algorithm.