Research On Sparse Linear Inverse Problems Based On Deep Networks

In many fields of scientific research and production areas such as image restoration,signal processing,and machine science,people often need to invert system information or recover input data from observation data,such problems are called inverse problems.The sparse linear inversion problem is an important problem in compressed sensing and sparse coding,and it is also a simplification and abstraction of many inverse problems.This paper focuses on solving the sparse linear inversion problem by using the deep network,and applying this model to the specific problems in reality to achieve better performance.The main work and innovations are as follows.(1)A cascading method is proposed to solve the problems that the dimension of input signal and the output signal are too different.When the input signal is too different from the output signal dimension and the problem of multiple linear transformations of signals,if the signal recovery is performed directly using a single deep network,the recovery effect will be poor.When the signal undergoes multiple transformations,if it is directly restored by a single network,some intermediate transformed signal information will be lost,resulting in a final recovery accuracy that is not good enough.In this paper,the signal recovery process is decomposed,which is equivalent to making a network cascade in the deep network,so that the output signal gradually reaches the dimension of the input signal,thereby greatly improving the accuracy of signal recovery.Experiments on random signals and image block datasets show that the convergence speed and recovery accuracy of the algorithm are improved.(2)Improve the application of linear sparse networks in image super-resolution and improve operational efficiency.Since the traditional ultra-sparse network needs to do a bicubic upsampling before input,this operation takes a lot of time during training and testing.Draw on the idea of other super-networks we improve the sparse network by replaceing the final convolutional layer with deconvolution or Sub-Pixel Convolutional,and change the deconvolution orSub-Pixel Convolutional parameters according to different expansion factors.Experiments have shown that the improved method can greatly speed up the operation efficiency,and the accuracy difference is less than 0.6dB.