Method of constructing measurement matrix based on cascade chaotic sequence

Abstract

The invention proposes a method of constructing a measurement matrix based on a cascade chaotic sequence and the method is mainly used for construction of a measurement matrix in compression perception. The processing of the method is as follows: firstly setting a specific parameter and setting an initial value to start iterating selected chaotic sequences; after iteration for a plurality of times, sequences V1, V2 and V3..., are obtained and then the iterated sequences are cascaded into one sequence V=[ V1, V2 and V3...]; then sampling the generated sequence at an interval of d and constructing an N*N matrix according to columns; and finally according to difference of M values, sequentially selecting columns from a first column to an Mth column so as to construct an M*N matrix and carrying out normalization on the matrix so that a measurement matrix Phi is obtained. The method effectively prevents a defect that a single chaotic matrix is degraded into a periodic sequence because of a computer precision problem and through a method of cascading of a plurality of chaotic sequences, the randomness of the chaotic sequence is strengthened so that the measurement matrix constructed by such a chaotic sequence has a signal reconstruction capability which is strengthened significantly.

Description

Technical field The invention relates to a method for constructing a measurement matrix based on cascaded chaotic sequences, and belongs to the technical field of compressed sensing. Background technique Compressed sensing is a new type of signal processing theory proposed by Candʻes and Tao in recent years. This theory uses the sparsity or compressibility of the signal to transform the traditional Nyquist sampling into random measurement sampling, and the Sampling and compression are performed at the same time, which successfully breaks through the Nyquist theorem's limitation on sampling frequency. The key part of the compressed sensing theory is the construction of the measurement matrix. A well-designed measurement matrix not only removes redundant information during the sampling process and retains useful information, but it can also reduce the number of measured values ​​and is conducive to accurate signal reconstruction. Random matrix is ​​currently the most com...

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Problems solved by technology

However, due to the difficulty and high cost of random matrix hardware design in practical applications, and its own defects such as uncertainty and large storage space, this is not conducive to the application of random matrices, while deterministic matrices such as partial Hadamard matrices, Although it has been proved that some Fourier matrices can reconstruct the original signal without distortion, the deterministic matrix is ​​often correlated with some sparse domains, so the deterministic measurement matrix is ​​also limited and not universal

As we all know, the chaotic sequence is the unity of randomness and determinism, and the chaotic system is not only simple in hardware design but also small in storage space, so the measurement matrix of the chaotic sequence construction came into being. However, due to the particularity of the chaotic system, if a chaotic sequence is in After many iterations, due to computer precision problems, the chaotic sequence will degenerate into a periodic sequence, which will affect the reconstruction effect of the signal.

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