A Deterministic Matrix Design Method Based on the Difference Set Modulo Subgroup for Computational Ghost Imaging

Abstract

Computational ghost imaging is a novel technique, which has a wide range of applications in many fields. As a key part of computational ghost imaging, the measurement matrix plays an important role in imaging quality and system practicability. To improve the imaging quality of computational ghost imaging and overcome the poor stability and non-negativity of the measurement matrix, we propose a new construction method for the deterministic measurement matrix based on the difference set modulo subgroup. This method uses an efficient simulated annealing algorithm to search for the difference set modulo subgroup. Then a 0–1 binary measurement matrix can be constructed according to the obtained difference set. We can show that the measurement matrix constructed by this method has low coherence and can satisfy the restricted isometry property. The simulation and experimental results showed that the reconstruction quality of the proposed measurement matrix was equivalent to the Sparse random matrix and better than the Toeplitz and Circulant matrices, which indicates the feasibility of the newly proposed measurement matrix.

Keywords

• Imaging system
• computational ghost imaging
• difference set modulo subgroup
• compressed sensing
• measurement matrix