Intelligent Matching Pursuit Sparse Reconstruction Method Based on Quasi-Newton Method

Abstract

The invention discloses an intelligent matching tracking sparse reconstruction method based on a quasi-Newton method. The steps are: modeling the compressed sensing reconstruction problem based on L0 norm minimization as finding an estimated support set of an original signal, where y is a measurement signal; Θ I is a subset of perception dictionaries consisting of columns corresponding to index values ​​in set I; is Θ I The violation operation; input variables, use the intelligent matching pursuit sparse reconstruction algorithm based on the quasi-Newton method to solve the optimization problem and intelligently search for the global optimal solution, and obtain the estimated support set I of the original signal * ;Using the least square method to calculate the reconstructed signal: where, is the value set of non-zero elements of the reconstructed signal; is the set of zero elements of the reconstructed signal. This method can effectively solve the L0 norm minimization problem, and has high reconstruction accuracy and fast 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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