Research On Quantized Compressed Sensing Based On Gradient Prior And Deep Image Prior

With the rapid development of science and technology,big data is gradually changing our lives.With the continuous improvement of people’s demand and quality of image information,image processing technology in different fields is also improving.Compressed sensing is an advanced signal acquisition technology.By utilizing the sparsity or compressibility of signals,it can accurately reconstruct signals from a small number of linear measurements,greatly reducing the requirements of data transmission,processing and storage,and providing a new research idea for the current large-scale image processing technology.However,image reconstruction itself is a NP-hard problem,and how to use prior information to reconstruct images is a hot research topic at present.In addition,signal acquisition,transmission and processing are inseparable from quantization,which is the only way to transform analog signal into digital signal.Therefore,it is necessary to study image reconstruction with quantitative background.Based on binary quantization as the core clue,this paper analyzes and models the prior information of images to improve the quality of quantized compressed sensing image restoration.The main work of this paper is summarized as follows:Based on the gradient sparsity of natural images,we propose a binary compressed sensing model with total variational minimization,and establish some theoretical results of robust recovery.We obtain the upper bound of recovery error and the lower bound of sampling numbers.Our theoretical results show that the direction and amplitude of any effective gradient sparse signal can be guaranteed to recover with high probability by total variational minimization.In addition,we propose several optimization algorithms for solving proposed models,and a large number of numerical experiments are carried out to verify the effectiveness of the algorithms.The results of this part fully excavate the gradient sparse structure of image signals,and provide a useful reference for the introduction of more image prior information and the design of measurement matrix.Total variation is a regularization term for encoding local smoothing prior structure of image,which is widely used in image processing.Based on the neural network image prior modeling,we propose a deep image prior quantized compressed sensing model with total variational regularization.On the one hand,this method takes advantage of the significant advantages of total variational regularization in image processing,on the other hand,it combines untrained neural network as a powerful image signal representation capability.Further,in order to solve the model effectively,we use the network architecture of the depth decoder and design the network projection gradient descent algorithm,and combined with a series of experiments to verify the effectiveness of our proposed method.