Research On Construction And Optimization Of Compressed Sensing Observation Matrix

Compressed sensing(CS)theory is a technology to reduce sampling time by reducing the number of sampling.This theory has made important progress in medical imaging,camera design,seismic monitoring,information theory,voice encryption and oil exploration.CS theory is a breakthrough to reveal a rule that can reduce the sampling time.Sparse signal can be reconstructed with high probability by using appropriate algorithm after using appropriate matrix for observation.Compressed sensing theory also needs us to design the appropriate observation matrix.The observation matrix needs to satisfy the conditions of linear independence,independent randomness and the equivalence of l₀ norm optimization and L₁ norm optimization in order to have better reconstruction effect.It is difficult to store the random matrix because of the harsh conditions of using partial orthogonal matrix.The deterministic matrix reduces the amount of information stored,but the reconstruction effect is not good.Under this background,this paper studies the construction and optimization of the observation matrix.This paper systematically summarizes the previous empirical research,and on this basis,obtains the construction and optimization method of the observation matrix:(1)After combining the properties of sparse random matrix and Vandermonde matrix,this paper proposes the construction method of observation matrix of sparse random block Vandermonde matrix,and concludes that sparse random block Vandermonde matrix can keep a certain reconstruction effect while reducing the storage space.(2)In this paper,the observation matrix optimization method based on Schmidt orthogonalization method is proposed under the condition of sparse basis orthogonalization.The conclusion is that the measurement matrix optimization based on Schmidt orthogonalization method has better reconstruction effect than before optimization.