Study On Sparse Signal Reconstruction Algorithm Based On ODE

In the network era,a large amount of data/signals are generated all the time,and people often need to conduct sampling and compression to realize the storage and transmission of these signals.Subsequently,it is extremely challenging to recover the original signal from the compressed signal,which also plays a key role in the practical application.Therefore,the sparse reconstruction technology has always been one of the research hotspots in the field of signal processing.Most of the traditional sparse reconstruction algorithm needs a lot of iterative arithmetic and high requirements for hardware computing power and storage capacity.The dynamic system based on ordinary differential equations(ODE)can be more quickly and efficiently.The existing dynamic systems only solve the sparse signal,but doesn't further enhance the convergence performance based on the control theory.In this paper,the ODE of dynamic system is modified to improve the convergence speed of the system.In addition,because the dynamic system has a significant advantage in solving the sparse reconstruction problem,this paper refers to this advantage in the traditional discrete iterative algorithm,and proposes several sparse reconstruction discrete algorithms by Euler method.The specific work is as follows:A dynamical sparse reconstruction algorithm with fixed-time convergence properties is proposed.Compared with the finite-time convergence dynamical system,this system increases the convergence speed of the system by adding an additional controller to the ODE.This system greatly shortens the convergence time and deviates from the initial conditions.A dynamical sparse reconstruction algorithm with fast fixed-time convergence properties is proposed.Compared with the fixed-time convergence dynamic system,the new system not only greatly improves the convergence speed but also has fixed time convergence.This system introduces an index function to measure the distance between all nodes in the current system state and the set threshold,and then selects the ODE at the next moment,thus simplifying the ODE control for each node and enhancing the flexibility of the systemThen six discrete iterative sparse reconstruction algorithms are proposed.In this paper,explicit Euler method and semi-implicit Euler method are used to discretization the exponential convergence system,the finite time convergence dynamic system and the fast fixed time convergence dynamic system.Compared with the traditional classical discretization algorithm,three of the algorithms significantly improve the convergence speed of sparse reconstruction.