# Deep Compressed Sensing Generation Model for End-to-End Extreme Observation and Reconstruction
## 1 Introduction
[19] were inspired by the generative models of VAE (auto-encoding variational) [20] and GAN (generative adversarial nets) [21]. They proposed the application of compressed sensing in the generative model (CSGM). Furthermore, it got rid of the constraint of sparsity with the help of the generative model of neural network. VAE or GAN learned the probability distribution of the dataset through pre-training. By compressed sensing, the difference of observation between the generated and real data is a loss function for backpropagation optimization. The results showed that the reconstruction effect was better than the traditional sparse reconstruction method for a smaller number of observations. In May 2017, [PERSON] [22] et al. proposed to extract a generative model that projected from low-dimensional to high-quality MR images using the pre-trained LSGAN framework. For undersampled observation data, the pre-trained generative model was used to improve fine texture details for more efficient image reconstruction. In 2018, [PERSON] [23] et al. proposed a compressed sensing reconstruction method based on deep image prior (DIP) without pre-training for the deep generative model. They introduced a regularization technique that incorporated prior weight information to reduce the reconstruction error. In 2019, [PERSON] [24] et al. proposed Deep Compressed Sensing (DCS), a generative model that did not require pre-training, and introduced a meta-learning method to train the generative model and the observation model jointly, achieving reconstruction through inner and outer loops of meta-learning, made the reconstruction response more flexible and rapid. In 2020, [PERSON] et al. [25] proposed a new sub-pixel convolution generative adversarial network to learn compressed sensing reconstruction of images. Through the adversarial training of the generative model of the sub-pixel convolution network and the discriminant model, the generative model learned the inherent image distribution and improved the reconstruction quality. Moreover, the low-dimensional observation vectors and the generative model could quickly reconstruct the image. In 2022, [PERSON] [26] proposed the combination of compressed sensing and deep neural networks. Compressed sensing theory was used to observe the recorded EEG data to reduce the computational load. Then, the observed data were classified according to the deep neural network, and the driver fatigue was effectively detected according to the classified results with a high accuracy rate. To sum up, traditional compressed sensing and reconstruction are limited by the sparsity constraint, which limits the expansion of their applications, and traditional reconstruction methods also consume time. With the development of deep learning, neural networks can directly extract hierarchical features from a given dataset to perform complex tasks in the real world [27]. The combination of deep learning techniques with compressed sensing, in which the hidden layer bearing of the neural network is used to compensate for the sparsity of signals so that it can be applied to data transmission and storage, is more likely to broaden its application field. Inspired by CSGM and DCS, this paper proposes a framework combining compressed sensing and deep learning to establish the correspondence of input and output (end-to-end deep compressed sensing using generative models, E2E_DCSGM) to achieve extreme observation and reconstruction. Observations of compressed sensing showed that the number of samples was significantly reduced, which was good for data transmission and storage. In the network model of reconstruction experiments, multi-layer perceptrons (MLP) and a deconvolution generative model (Deconv_Net) were used in combination with an untrainable observation matrix (A), a trainable observation matrix (A trainable, AT), and a deep compressed sensing observation network of multi-layer perceptron (A deep trainable, ADT). In the MNIST experiment, the generative model was MLP, and the observation models were A, AT, and ADT.