Intelligent matching pursuit sparse reconstruction method based on quasi-Newton method

Abstract

The invention discloses an intelligent matching pursuit sparse reconstruction method based on a quasi-Newton method. The method includes steps of modeling the compressed sensing reconstruction problembased on L0 norm minimization as a formula as described in the description finding the estimated support set of the original signal, where y is the measurement signal; theta I is a perceptual dictionary subset composed of columns corresponding to the index values in the set I; a formula as described in the description is a violation of. Theta. I; input variable. An intelligent matching pursuit sparse reconstruction algorithm based on quasi-Newton method is used to solve the optimization problem a formula as described in the description, obtaining an estimated support set I* of the original signal; calculating the reconstructed signal using the least square method: a formula as described in the description wherein, a formula as described in the description is that set of non-zero element value of the reconstruction signal; a formula as described in the description is a collection of zero element of that reconstructed signal. This method can effectively solve the L0 norm minimization problem with high reconstruction accuracy and high reconstruction speed.

Description

technical field [0001] The invention belongs to the technical field of compressed sensing, and in particular relates to an intelligent matching and tracking sparse reconstruction method based on a quasi-Newton method, which is used to effectively solve the problem of minimizing the L0 norm in compressed sensing reconstruction. Background technique [0002] In order to break through the limitations of the Nyquist sampling theorem, Candes and Donoho proposed a new theoretical framework for signal sampling transmission in 2006, namely Compressive Sensing (CS) theory. The CS theory points out that if the original signal is sparse or compressible, the accurate original signal can be reconstructed by a sampling frequency much lower than the Nyquist sampling theorem, which greatly relieves the pressure on sampling hardware and transmission bandwidth. It is widely used in many fields. The CS framework mainly includes three main processes: (1) Sparse representation: use a sparse bas...

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Problems solved by technology

[0016] Through the above description, the minimization of the L0 norm is the essential problem of compressed sensing reconstruction, which can obtain the sparsest solution, and the number of measurements required for accurate reconstruction is small, but it belongs to the NP-hard combinatorial optimization problem, and the computational complexity is huge , the greedy algorithm used to solve the L0 norm minimization problem tends to fall into local optimum, and the reconstruction accuracy is low. For this kind of problem, this case arises

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