Research On Joint Block Sparse Decomposition Algorithm Based On Dictionary Learning

Compressed Sensing(CS)is a new type of signal compression sampling method.Under the condition that the signal itself is sparse or can be sparsely expressed under a certain domain,the signal can be obtained by under sampling at a very low sampling rate.Measure the value and then use some mathematical method for accurate reconstruction.With the deepening of research and the complexity of actual signal processing scenarios,common sparse structures and single-antenna signal scenes are far from satisfying the application of compressed sensing in real-world scenarios.Based on this,block sparse theory [2,3] and Distributed Compressed Sensing(DCS)has emerged,which broadens the application range of compressed sensing.The problem to be solved by sparse decomposition is to find the sparsest representation of the signal in a given dictionary,thus simplifying the structure of the original signal and facilitating analysis and processing.In recent years,sparse decomposition theory has been obtained in the fields of spectrum sensing and image denoising.A good application.Dictionary learning and sparse decomposition are complementary.The sparse coefficients obtained by sparse decomposition serve dictionary update,and the improved dictionary can obtain better sparse decomposition performance.Considering the actual multi-antenna scene,the signals received by each antenna mostly exhibit the characteristics of sparse coefficient block distribution.We apply the block sparse model to DCS and propose a more generalized joint block sparse model.For the better sparse decomposition effect of the model,we apply the dictionary learning algorithm to the proposed sparse decomposition algorithm and achieve good results.Therefore,the research content of this paper mainly includes the following three aspects:Firstly,the basic theory of block sparseness and DCS is introduced.The four joint sparse models(JSM)in DCS are introduced in detail,and the JSM-2 widely used in communication signal processing is given.Schematic diagram of two models of G-JSM.At the same time,three block dictionary learning algorithms are introduced,and their degree of improvement on block sparse decomposition performance is compared by simulation.These models and algorithms are the basis for our follow-up studies.Secondly,the sparse decomposition algorithm under JSM-2 and G-JSM joint sparse models is systematically studied.In the JSM-2 model,the detailed process of SOMP algorithm is introduced,especially the strategy of atomic selection.The sparse decomposition performance of OMP algorithm under different SNR is compared,and the number of signals and the measured value are two.The effect of sparse decomposition performance of the algorithm is selected to select an algorithm more suitable for signal sparse decomposition in this model.Under th e G-JSM model,the Joint OMP algorithm and the principal component analysis method based on the minimum description length are introduced.The latter can realize the blind reconstruction of the common part of the signal under the G-JSM model.We compare these algorithms through simulation.The performance of the algorithm selects the best algorithm for the sparse decomposition of the common part of the signal under the G-JSM model.Finally,the block sparse model is combined with the joint sparse model,and a joint block sparse model based on JSM-2 and G-JSM is proposed.The simulation diagrams of the two models are given.At the same time,the B-SOMP algorithm is proposed.The sparse decomposition problem under the model is solved.The simulation results show that the proposed algorithm can solve the sparse decomposition problem of the proposed model.Considering the problem of high computational complexity of the traditional block dictionary learning algorithm when the sample size is large,an online dictionary learning algorithm(ODL)widely used in machine learning is introduced and applied.In the proposed sparse decomposition algorithm,the simulation results prove the feasibility of the ODL algorithm.Then,the simulation compares the performance of the ODL algorithm and the three block dictionary learning algorithms to achieve the purpose of selecting the appropriate dictionary learning algorithm under different conditions.