Research On Weighted L₁ Minimization Model Via Combining Prior Information And Learning Mechanism

Compressed sensing theory breaks through the limitations of the Nyquist sampling theorem and can accurately reconstruct signals with a small number of measurements.Reconstruction algorithm is an important part of the theory of compressed sensing.The performance of reconstruction is a key indicator of the application of compressed sensing theory.Effective use of the a priori information of the signal can improve the performance of the compressed sensing reconstruction algorithm.However,there is a bottleneck in the research of compressed sensing reconstruction algorithm.The prior information of the signal is extracted by manual observation or mathematical statistical analysis.However,the prior information extracted by these methods belongs to the shallow prior information and may be ignored.Lose more valuable a priori information.Therefore,with the help of deep learning and powerful learning ability,this paper mines the a priori information of the deep signal by training the depth model,and integrates the deep signal prior information of the extracted signal into the reconstruction algorithm of compressed sensing to improve the reconstruction.The purpose of signal accuracy.Using deep learning tools to mine the a priori information of deep signal can break through the bottleneck of current compressed sensing reconstruction algorithm,which is of great significance for the research of compressed sensing reconstruction algorithm.This paper is a study of the weighted l₁-norm minimization model of joint prior information and learning mechanism.The main work has the following aspects:（1）Solving for the weighted l₁-norm minimization model.Based on the iterative soft threshold algorithm,this paper proposes a weighted l₁-norm sequence iterative soft threshold algorithm（weighted l_1SISTA）.The purpose of weighting is to integrate other prior information of the signal to accurately reconstruct the signal.After experimental comparison,the reconstruction performance of the weighted l_1SISTA algorithm is significantly better than other algorithms in the case of less measured values.（2）Focusing on acquiring the deep prior information of the signal,in order to solve the bottleneck encountered by the current reconstruction algorithm,a learning mechanism is introduced.The purpose is to automatically mine the a priori information of the signal through the machine,and provide more valuable for the reconstruction algorithm.A priori information.This paper proposes to map the solution framework of the weighted l_1SISTA algorithm into the RNN（cyclic neural network）model to form the weighted l_1SISTA-RNN model.The weighted l_1SISTA-RNN model parameters are derived from the parameters of the weighted l_1SISTA reconstruction algorithm.The input of the model is the measurement of the sequence signal,the model output is the reconstructed signal,and the initial sequence signal is used as the training set.Using the data pair weighted l_1SISTA-RNN model training,the model will update the parameters,and the updated parameters are the mathematical expression of the signal deep prior information.Finally,the deep prior information obtained by learning is used for signal reconstruction.Experiments show that the model performs better than other algorithms in reconstructing signals from Caltech-256 image dataset and PTB ECG dataset.