# Binary Ghost Imaging Based on the Fuzzy Integral Method
###### Abstract  
The reconstruction quality of binary ghost imaging depends on the speckle binarization process. In order to obtain better binarization speckle and improve the reconstruction quality of binary ghost imaging, a local adaptive binarization method based on the fuzzy integral is proposed in this study. There are three steps in the proposed binarization process. The first step is to calculate the integral image of the speckle with the summed-area table algorithm. Secondly, the fuzzy integral image is calculated through the discrete Choquet integral. Finally, the binarization threshold of each pixel of the speckle is selected based on the calculated fuzzy integral result. The experiment results verify the feasibility of the proposed method. Compared with other methods qualitatively and quantitatively, the proposed method has high performance in reconstructing image of target. binary ghost imaging; fuzzy integral algorithm; discrete Choquet integral; imaging resolution 202116162. 11. Therefore, GI has been widely used in the field of multispectral imaging [9; 10; 11], terahertz imaging [12; 13; 14], remote sensing [15; 16; 17], and laser RADAR [18; 19; 20; 21; 22; 23]. However, the low imaging speed brings unprecedented challenges to the practical application of GI. A substantial amount of measurements are required to guarantee the high-quality of reconstructed results of targets. Fortunately, with the compressive sensing and deep learning algorithms being widely applied in GI, compressive sensing ghost imaging (CSGI) [24; 25; 26; 27; 28] and deep learning ghost imaging (DLGI) [29; 30; 31; 32; 33] can reconstruct intensity images of targets with high quality under extremely low sampling conditions. This enables CSGI and DLGI to have high frame frequency imaging and even real-time video imaging. In the GI system, the laser speckle distribution and total reflected laser intensity need to be measured by spatial resolution detector and single pixel detector, respectively, resulting in the measurements of the two categories of detectors which can be correlated to calculate the intensity distribution of the target. Generally, the data sizes of laser speckle distribution and total reflected laser intensity are huge, which leads to extreme inconvenience of the storage and transmission of data, and further decreases the imaging frame frequency. In order to reduce the data sizes for facilitating the storage and transmission, the ghost imaging with two quantization levels of signal processing, so called binary ghost imaging (BGI), is proposed to compress the recorded information [34; 35; 36; 37; 38]. Although, BGI greatly compresses the size of data, the consequent problem is the loss of measurement information, which reduces the imaging quality. Therefore, how to binarize the measurements to ensure the minimum loss of information has been an interesting topic. Many research groups proposed their binary schemes to improve the imaging quality of BGI, such as mean binarization ghost imaging (MBGI) [36], Otsu binary ghost imaging (OBGI) [37], and point-by-point binary ghost imaging (PPBGI) [38]. The mutual problem encountered by the above methods is that the reconstructed imaging quality of BGI based on the global binarization methods is relatively low, while the reconstructed imaging quality of BGI based on the local method requires a long binarization time. Inspired by the fuzzy integral method, successfully applied widely in the fields of classification, foreground detection, and data modelling [39; 40; 41; 42; 43], a high-resolution and short reconstruction time BGI based on fuzzy integral method (FIBGI) is proposed in this paper. The fuzzy integrals can be thought of as the general representation of the image filter [44]. A large number of common image filters, such as linear filters, stack filters, and morphological filter can be represented by the fuzzy integrals. The fuzzy integrals integrate a real-value function with respect to fuzzy measures, which are generalizations of probability measures.