High-quality object reconstruction based on ghost imaging

Ghost imaging (GI) becomes an attractive research topic in recent years, and has been developed for some years. Correlation algorithm is usually used to reconstruct object in the GI. However, due to a linear relationship between quality of the recovered objects and the number of measurements, it needs a large number of measurements to obtain a satisfied object reconstruction when conventional GI is applied. Although some improved algorithms, e.g., differential GI and normalized GI, are developed, they could still not be feasible for achieving high-quality object reconstruction in some cases. In this paper, a high-quality object reconstruction method is presented for the GI. The method takes advantage of the property of Hadamard transform. For a 2D matrix, after the Hadamard transform is applied to it, the first element of the Hadamard spectrum is equivalent to the sum of all matrix elements. In the measurement process of GI, single-pixel detector collects the total light intensity, i.e., the sum of transmitted light. Hence, the property of Hadamard transform corresponds to the single-pixel measurement process in the GI. As a result, it is possible to utilize the detected single-pixel values as constraints. An algorithm is presented in this paper to reduce the number of measurements dramatically in the GI and simultaneously achieve a high-quality object reconstruction. In the method, the signal-to-noise ratio (SNR) has a nonlinear growth with respect to the number of measurements, and it is different from conventional GI methods. Feasibility and effectiveness of the method are computationally demonstrated.