Fast compressive imaging using scrambled block Hadamard ensemble

With the advent of a single-pixel camera, compressive imaging applications have gained wide interests. However, the design of efficient measurement basis in such a system remains as a challenging problem. In this paper, we propose a highly sparse and fast sampling operator based on the scrambled block Hadamard ensemble. Despite its simplicity, the proposed measurement operator offers universality and requires a near-optimal number of samples for perfect reconstruction. Moreover, it can be easily implemented in the optical domain thanks to its integer-valued elements. Several numerical experiments show that its imaging performance is comparable to that of the dense, floating-coefficient scrambled Fourier ensemble at much lower implementation cost.