The Research And Applications Of Matching Pursuit Algorithm Based On Adaptive Gabor Subdictionary In Image Sparse Decomposition

Matching pursuit algorithm is a typical iterative greedy algorithm,In order to reduce the difficulty of obtaining the optimal solution,it is a method to obtain the suboptimal solution.Each iteration is selected to approximate the residual signal in the atom dictionary which is the most matched with the residual signal(the best correlation).It is the most obvious feature of the matching pursuit algorithm to pursue the fastest decline of the residual signal energy in each iteration.The decomposition coefficient obtained by matching pursuit algorithm is not as sparse as that of the base pursuit algorithm,but its effect has not been very different.Generally speaking,two different sparse representation algorithms are used to decompose the same signal with the matching pursuit algorithm and the base pursuit algorithm respectively.The former has more obvious advantages than the latter in both the complexity of the algorithm and the calculation speed.In this paper,the traditional matching pursuit algorithm is improved,and the improved algorithm is used to sparse representation and decomposition of the image signal,and good results have been achieved.Usually,the amount of computation and storage required by the sparse decomposition algorithm for image processing is very huge.It is often unbearable under the computing speed and storage space of the existing computer.These restrictions seriously affect the popularization and application of the theory of signal sparse representation.For the traditional matching pursuit algorithm,the overcomplete atomic dictionary must be determined beforehand.The larger the number of atoms in the overcomplete dictionary is,the more sparse the structure of the signal decomposition is,but this will give the algorithm a higher requirement on the amount of computation and storage.This big limit makes the generalization of the traditional matching pursuit algorithm and the extension of the traditional matching pursuit algorithm.Application.Most of the improved algorithms are mainly based on the search for better atomic search methods or the application of more multi parameter optimization methods to the algorithm.Through these improvements,the algorithm reduces the computational complexity and storage space to a certain extent.However,how to make full use of the characteristics of the atom itself in the dictionary and the structure characteristics of the dictionary to improve the performance of the algorithm is also a very important research direction in the design of search strategy and the search for optimization algorithms.The author of this article has mainly done the following work:(1)The characteristics of the image signal are analyzed systematically.Because of the visual,coding and psychological redundancy of the image signal,the sparse decomposition method is more suitable for the representation and compression of the image signal than the traditional base decomposition method.(2)There are many algorithms for sparse representation,such as frame method,combinatorial method,base pursuit algorithm and matching pursuit algorithm…….By analyzing and testing the characteristics of the image signals,the authors conclude that the matching pursuit algorithm is more suitable for sparse representation of image signals.(3)To study the sparse representation,such as the Gabor dictionary,the Chirplet dictionary,the FMlet dictionary,the Dopperlet dictionary and other common dictionaries,compared to the other atoms,the structure of the Gabor atom determines that its time-frequency aggregation is the best,and the expressed image is thinner and thinner.In view of this,Gabor overcomplete dictionary is selected in this paper.(4)The traditional matching pursuit algorithm always uses a fixed and overcomplete dictionary,which makes the iteration times of each iteration in the matching atom process are the same,the amount of computation is great,and the self-adaptive is not.The sub dictionary used in the improved algorithm is made in real time during the decomposition process,so that it can reduce it.The required amount of calculation and storage capacity.(5)The atoms in the dictionary are discretized,and then the fast Fourier transform(FFT)can be applied to the algorithm.The calculation of inner product is replaced by cross-correlation operation,so as to reduce the amount of computation needed to match.(6)With the help of MATLAB platform,the same image is represented by the improved algorithm and the traditional algorithm respectively.Compared with computer processing speed,computer storage requirement and image quality reconstruction,etc.The true result is to verify the reasonableness of the analysis.(7)Use the method described in this paper and the base decomposition method(JPEG and JPEG2000)respectively for the same image.It shows that we compare them from different angles and draw a conclusion.