Ghost imaging (GI) is a new imaging technique that extracts object information by measuring the intensity coherence of the light field. In recent years, GI has attracted a lot of attention because it has been shown to be achieved by thermal and other new sources [1], [2], [3] and is now used in many applications such as remote sensing [4], [5], scattered medium imaging [6], [7], spectral imaging [8], [9], photon-limited imaging [10], [11], X-ray imaging [12], [13], and so on.

Reconstructing high-quality images at low sampling rates is a key challenge in pseudo-thermal ghost imaging [14]. Scholars have proposed two methods to address this issue: the improved second-order correlation method [15], which improves the signal-to-noise ratio of the reconstructed image, and the method based on compressed sensing (CS) [16] theory, which utilizes the sparse property of the image. The latter method generally has better performance than the former [17].

Recently, it has been shown that the image reconstruction quality of ghost imaging is affected by the sampling efficiency, i.e., how much “valuable” information is obtained by sampling [18]. A high sampling efficiency means that more useful information can be obtained with the same number of samples, and thus better image reconstruction can be obtained. Therefore, a key issue in GI is how to improve the sampling efficiency, and the problem of improving the sampling efficiency can be translated into the light field optimization problem, which is also the optimization problem of the sampling matrix in compressed sensing. So far, many kinds of light field optimization schemes have been devised, and these speckle patterns optimization schemes can be broadly classified into two categories, one is fixed speckle patterns, such as sinusoidal patterns and Hadamard patterns [19], [20], and the other is adaptive speckle patterns learned for a specific data set, such as the basis matrix obtained by dictionary learning, and the patterns are subsequently calculated by matrix optimization [21], [22].

A measurement-driven framework for dictionary learning is proposed in [23], which differs from the traditional dictionary learning framework. Under this new framework, the sparse matrix is calculated based on the measured values, rather than being updated along with the dictionary matrix. The application of this framework in ghost imaging is demonstrated in [24], where it leads to good results, but there is still room for improvement in imaging quality at low sampling rates when the sampling rate is low. The poor imaging quality at low sampling rates is caused by the non-negligible correlation between adjacent light fields when the light fields are learned using this method. To address this issue, we apply the low-rank matrix decomposition method [25], which is commonly used in video background modeling to extract the background of a video by utilizing the correlation between video frames, to optimize the optical fields for ghost imaging, thereby extracting the correlation information between the optical fields and improving the imaging quality.

In this work, we improve imaging quality at low sampling rates by imposing low-rank constraints on the learned light field using a measurement-driven framework. We also investigate the impact of sparse representation error (SRE) on the optimized light field and find that the reconstruction results of the light field learned using this framework are highly robust to SRE.