Research On Depth Expansion Model Based On Weighted L1-L1 Minimization

As a novel data processing method,compressed sensing has been widely used in fields such as biomedical engineering,computer vision,and pattern recognition.As one of the most important links in compressed sensing theory,the reconstruction algorithm is directly related to the accuracy of the signal reconstruction,so it has become the focus of many scholars.Among them,l1-l2 minimization is widely known as a classic method that uses the sparsity and similarity between sequence signals to solve the problem of sequence sparse reconstruction.However,l2 regularization is very sensitive to outliers.Due to its excessive suppression of the information contained in the outliers,it often fails to greatly improve the quality of reconstruction.Based on this,this article aims to design a new model algorithm to alleviate this problem.The main research content and contributions include the following:(1)Taking the deficiencies of the l1-l2 minimization algorithm as the basic point of the problem,this paper proposes a new algorithm framework based on the weighted l1-l1 norm minimization to solve the problem of sequence sparse reconstruction.Our algorithm conception is mainly considered from the following aspects:initially,compared to the l2 norm,the l1 norm is less sensitive to outliers.Secondly,in many scenarios in real life,the errors between adjacent signals mainly follow the Laplace distribution rather than the Gaussian distribution.We analyze and derive the convergence of the proposed algorithm,and further propose an improved algorithm.By introducing the filtering principle into the algorithm iteration process,the sparse dictionary can be optimized in size,thereby reducing the running time of the algorithm,improved algorithm efficiency.(2)By expanding the time step and number of iterations of the solution algorithm,we mapped the entire algorithm flow into a recurrent neural network(RNN),that is,the W-l1-l1RNN model.Since the entire network framework is implicitly defined by the algorithm process,we can also use the strong learning ability of the neural network to update the parameters with data and mine deeper prior information while retaining the known prior information.Through experiments on the Caltech-256 data set and the PTB diagnostic ECG data set,we have proved that the W-l1-l1-RNN model performs better than some advanced model-based methods and some classic deep learning-based methods.The method also proves that the W-l1-l1-RNN model with interpretability requires much less training data than the traditional "black box" neural network.Finally,we also proved our point of view through experiments,that is,the reconstruction effect of the algorithm based on l1-l1 minimization on outliers far exceeds that of the algorithm based on l1-l2 minimization.