Compressed Sensing Via A Deep Convolutional Auto-encoder

The Nyquist-Shannon sampling theorem states that a bandlimited continuous-time signal can be sampled and perfectly reconstructed from its samples if the waveform is sampled over twice as fact as the highest frequency component.It establishes a fundamental bridge between analog signals and digital signals.However,with the development of the era of big data,the acquisition and transmission of signals encounters enormous chanllenges wherefore the lage number of samples specified by the Nyquist-Shannon sampling theorem hinders the fast acquisition and transmission of signals.In the past few decades,the development of compressed sensing(CS)has attracted widely concern in the fields of signal processing,applied mathematics and computational photography since it ensures the possibility that signals may be acquired surpassing the limits of Shannon-Nyquist sampling theorem.The theory of CS builds upon the precondition that the signals has sparsity properties which provides the basis for the signals to be sampled with small number of measurements and guarantees perfect reconstruction.In practical application of CS,random sampling and nonlinear optimization algorithms are usually developed to implement the phases of compressed sensing and signal reconstruction respectively.After a long period of research,random sampling and nonlinear recovery are not promising in accuracy and speed at a low sampling rate,which limits the practical usage of compressive sensing.This paper proposes a deep learning-based CS framework which leverages deep fully convolutional auto-encoder for image sensing and recovery.The utilized auto-encoder consists of three components: the fully convolutional network is learned for image sensing in the encoder,while in the decoder,the deconvolutional network and refined reconstruction network are learned for intermediate and final recovery,respectively.Different from most previous work focusing on the block-wise manner to reduce implementation cost but result in blocky artifacts,our adaptive measurement matrix is applicable to any size of scene image and the decoder network reconstructs the whole image efficiently without any blocky artifacts.Moreover,dense connectivity is leveraged to combine multi-level features and alleviate the vanishing-gradient problem in the refined reconstruction network which boosts the performance on image recovery.Compared to the state-of-the-art methods,our algorithm improves more than 0.8dB in average PSNR.