## 1 Introduction  
Single-cell RNA sequencing has become increasingly popular in transcriptome research [1] owing to its ability to reveal gene expression at single-cell resolution [2], which can help researchers study cellular heterogeneity and complexity. This technology has been applied to many areas, such as the classification of novel cell subtypes [3, 4, 5], differential gene expression analysis [6, 7], spatial reconstruction [8, 9], and development trajectories [10, 11]. Compared to bulk RNA sequencing, single-cell RNA sequencing has higher resolution, which can better reflect the heterogeneity across cells. However, the single-cell transcriptome sequencing data is sparse due to the low starting amount of transcripts, which increases the likelihood of missed transcripts during the reverse transcription steps [12, 13]. Thus, the transcripts cannot be detected in the later step of sequencing, resulting in the count appearing as zero, which is called the dropout event. Specifically, some genes are expressed in some cells but not in others of the same type. It is necessary to note that not all zeros in single-cell RNA data can be considered dropout values. A zero value for a gene in a cell could be biological zeros, which mean the true absence of transcripts or mRNAs. The biological zeros can be produced by cell type-specific expression or by the phenomenon that many genes are transcribed intermittently [14, 15]. Furthermore, the scRNA-seq platform used, the depth of sequencing, and the potential expression level of the gene can influence the degree of sparsity [16]. The generation of biological and non-biological zeros results in a proportion of zeros in the scRNA-seq data as high as 90% [17], which poses challenges for downstream computational analyses [13]. To better perform downstream analysis, it is necessary to impute the scRNA-Seq data. Several scRNA-seq-specific imputation methods from multiple angles have been proposed to solve the problem of sparsity and improve downstream analysis. According to [PERSON] et al. [16], it can be divided into three categories without external reference. The three categories include model-based imputation methods [17; 18; 19; 20; 21], data-smoothing methods [22; 23], and data-reconstruction methods [24; 25; 26; 27; 28]. Model-based imputation methods assume that the scRNA-seq data conform to a distribution. Based on the properties of scRNA-seq data, some models are designed to model the distribution of the scRNA-seq data, such as decreasing logistic function [18], Gamma-Normal mixed model [19], negative binomial (NB) model [17], zero-inflated negative binomial (ZINB) model [21], and so on. Data-smoothing methods impute the data using information from similar cells. They are usually imputed with zero values. Data-reconstruction methods usually use matrix decomposition [24; 25] or machine learning methods [26; 27; 28] to reconstruct data and these three methods usually overlap. Most of these methods impute the data by leveraging information on the similarity of cells or the correlations of genes. For instance, after detecting possible dropout values using the Gamma-Normal mixed distribution model, scImpute [19] takes advantage of information among similar cells to impute the data through non-negative least squares regression. VIPER [20] preserves gene expression by leveraging information from cells with similar expression patterns rather than using information from the same subpopulation, which uses a sparse non-generative regression model to actively select the sparse set of local neighborhood cells that are most predictive of the cells to be imputed. DeepImpute [26] employs a deep neural network along with dropout layers and a loss function, using information from correlated genes to learn patterns for imputing \"target genes.\" DeepImpute adopted a dive-and-conquer strategy in the deep learning imputation process for its efficiency by constructing multiple sub-neural networks. scRecover [21] assumes that scRNA-seq data follows the ZINB distribution.