A specific measurement matrix in compressive imaging system

Compressed sensing or compressive sampling (CS) is a new framework for simultaneous data sampling and compression which was proposed by Candes, Donoho, and Tao several years ago. Ever since the advent of a single-pixel camera, one of the CS applications - compressive imaging (CI, also referred as feature-specific imaging) has aroused more interest of numerous researchers. However, it is still a challenging problem to choose a simple and efficient measurement matrix in such a hardware system, especially for large scale image. In this paper, we propose a new measurement matrix whose rows are the odd rows of N order Hadamard matrix and discuss the validity of the matrix theoretically. The advantage of the matrix is its universality and easy implementation in the optical domain owing to its integer-valued elements. In addition, we demonstrate the validity of the matrix through the reconstruction of natural images using Orthogonal Matching Pursuit (OMP) algorithm. Due to the limitation of the memory of the hardware system and personal computer which is used to simulate the process, it is impossible to create such a large matrix that is used to conduct large scale images. In order to solve the problem, the block-wise notion is introduced to conduct large scale images and the experiments results present the validity of this method.