## 1 Introduction  
Digital halftoning is a special technique of converting a continuous image into a binary image, which is widely used in many fields, such as printing industry, textile industry and the electronic display field [1,2]. The binary image, called halftone image, can simulate the original continuous tone image in bi-level output devices. However, when halftone images need to be further processed by applying general image methods, such as image zooming, rotation, compression, and feature extraction, they are typically difficult to operate. Thus, another technique named inverse halftoning comes into being for this purpose. Inverse halftoning is a technique which is used to reconstruct a continuous tone image from its corresponding halftone image. Due to a certain amount of information loss in the process of digital halftoning, inverse halftoning is an ill-posed problem. Thus, reconstructing a high-quality continuous tone image from its halftone version is a challenging but promising research topic. Over the past several decades, many inverse halftoning methods have been presented. The proposed methods can be classified into five categories: filtering, deconvolution, optimization estimation, vector quantization, and machine learning [1,2]. The filtering-based method includes Gaussian low-pass filtering method [3], adaptive filtering [4], linear or non-linear filtering [5], and transform-domain filtering [6]. The low-pass filtering is a simple and fast inverse halftoning method, it can remove most of the noise in the reconstructed continuous tone image. Nevertheless, it also causes edge blurring. Besides low-pass filtering, other filtering-based methods, such as adaptive filtering, linear or non-linear filtering, and transform-domain filtering, are designed for obtaining a sharp image with a low perceived noise level. Although these methods can produce good results on image edges, they also create artifacts in the image smooth areas. Inverse halftoning can be considered as a deconvolution problem, which was first proposed by [PERSON] et al. [7] as a linear approximation model. This method can work well for images generated by error diffusion halftoning method but does not apply to other types of halftone images. [PERSON] et al. [8] proposed a novel inverse halftoning by applying classified vector quantization, it is also effective for error diffusion halftoning. The machine-learning-based inverse halftoning method is to train a model by using continuous tone images and their halftone versions, and then the continuous tone value can be estimated by this model. The model includes neural network [9; 10], sparsity-based [1; 11; 12], and look-up table [13; 14]. Compared to other two machine-learning-based methods, the method based on look-up table is a promising method because of its fast speed and universality. Thus, it has attracted the attention of many researchers. The method based on look-up table was first proposed by [PERSON] et al. [13] for inverse halftoning. Since then, many methods were proposed to improve the performance of this method [14; 15; 16; 17; 18; 19; 20; 21; 22]. In summary, the improvements include three aspects. The first is the template selection and optimization [14; 15], where the correlation method and the elitist genetic algorithm were used to obtain the best template. The second is to reduce the size of the table and improve the speed of searching look-up table [16; 17; 18; 19], while the third is to get the accurate contone value from each template pattern [20; 21; 22]. Although these improvements have produced relatively satisfactory results for grey images, very little research has addressed color inverse halftoning. Except for references [13] and [14], most of the existing color inverse halftoning methods are a simple extension of the look-up table (LUT) method to each color planes separately. Since these color inversing methods cannot consider the correlation between the color planes, they lead to a poor quality of color continuous-tone images.