# Serial Decoders-Based Auto-Encoders for Image Reconstruction
## 2 Related Research  
Narrow auto-encoders-based data compression and signal compressing have progressed rapidly [7; 8; 12; 13; 14; 19; 20; 21]. Firstly, auto-encoders have been studied and applied in the compression of medical signals, navigation data, and quantum states [7; 12; 13; 19]. For example, [PERSON] et al. proposed an auto-encoders-based compression method of brain neural signals [7]. [PERSON] et al. utilized convolutional auto-encoders to compress electrocardio signals [12]. [PERSON] et al. employed linear auto-encoders to compress navigation data [19]. [PERSON] et al. used quantum auto-encoders to compress quantum states [13]. Secondly, auto-encoders have already been studied and applied in the compressed sensing of biomedical signals, images, and sensor data [8; 14; 20; 21]. For instance, [PERSON] et al. utilized stacked and label-consistent auto-encoders to reconstruct electrocardio signals and electroencephalograms [8]. [PERSON] et al. used binary  
Figure 1: Data reconstruction performance using AAE. auto-encoders for compressed sensing of neural signals [20]. [PERSON] utilized auto-encoders to reconstruct magnetic resonant images [21]. [PERSON] et al. adopted sparse auto-encoders to reconstruct sensor signals [14]. Important developments in narrow auto-encoders also include the following: the Wasserstein auto-encoder, the inverse function auto-encoder, and graphical auto-encoders [15; 16; 22]. For example, [PERSON] et al. raised Wasserstein auto-encoders, which are generalized adversarial auto-encoders, and utilized the Wasserstein distance to measure the difference between data model distribution and target distribution, in order to gain better performance in data reconstruction than classical variational auto-encoders and adversarial auto-encoders [15]. [PERSON] et al. employed inverse activation function and pseudo inverse matrix to achieve the analysis representation of the network parameters of auto-encoders for dimensional reduction and reconstruction of image data, and hence improve the data reconstruction performance of auto-encoders [22]. [PERSON] presented graphical auto-encoders, used graphical regularization for data de-noising, clustering and classification, and consequently attained better data reconstruction performance than classical auto-encoders [16]. Generalized auto-encoders-based data compression and signal-compressed sensing have also achieved significant evolution [9; 10; 23]. These methods usually utilize multi-level auto-encoders to overcome the disadvantage that single-level auto-encoders have in being unable to achieve lossless data reconstruction; these methods use auto-encoders to replace one unit of the classical data compression and signal-compressed sensing model, such as the prediction, transformation, or quantization unit of data compression, as well as the measurement or recovery unit of signal-compressed sensing. For instance, [PERSON] et al. applied two-level auto-encoders for image compression. The first-level auto-encoders compress image blocks, and the second-level auto-encoders compress the recovery residuals of the first-level auto-encoders. This approach makes up for the disadvantage that single-level auto-encoders have in being unable to implement lossless data reconstruction to a great degree [9]. [PERSON] et al. adopted multi-level auto-encoders to implement the transformation coding unit of video compression. The first-level auto-encoders compress the prediction residuals, and the next-level auto-encoders compress the reconstruction residuals of the previous-level auto-encoders to a great extent [10]. [PERSON] et al. employed auto-encoders to implement the prediction coding unit of compressed sensing of sensor signals [23]. The main research advances in generalized auto-encoders also comprise the use of other architectures of deep neural networks to implement data compression and signal-compressed sensing [24; 25; 26; 27].