Image encryption method based on multi-scale compressed sensing and Markov model

An image encryption method based on multi-scale compressed sensing and a Markov model, comprising:

• generating parameters and initial values of one-dimensional chaotic mapping according to plaintext image information;
• obtaining subsampling rates of original coefficient matrices at all levels by using multi-scale block compressed sensing theory through a total target sampling rate of a plaintext image;
• substituting the parameters and initial values of the one-dimensional chaotic mapping into a corresponding chaotic system to generate chaotic sequences, transforming the chaotic sequences into a matrix form, and obtaining corresponding orthogonal basis matrices, and extracting some elements of the orthogonal basis matrices as measurement matrices according to the subsampling rates;
• performing three-level discrete wavelet transform on the plaintext image to obtain the original coefficient matrices at all levels, and blocking the original coefficient matrices at all levels to construct new coefficient matrixes at all levels;
• using the chaotic sequences to generate index sequences, and scrambling the corresponding coefficient matrices at all levels as blocks;
• using the measurement matrices to measure the coefficient matrices at all levels;
• retaining low-frequency coefficient matrices, merging measured non-low frequency coefficient matrices at all levels to construct a matrix T, performing micro-processing on the matrix T to obtain a to-be-measured matrix NT, and respectively generating a row-state transition probability matrix and a column-state transition probability matrix according to the to-be-measured matrix NT;
• performing SVD decomposition on the low-frequency coefficient matrices to obtain submatrices, and quantizing the elements in the submatrices and the non-low frequency coefficient matrices at all levels to a preset interval;
• generating index values according to the information of the chaotic sequences and determining merging rules by the index values, firstly mering the non-low frequency coefficient matrices at all levels according to the merging rules to obtain an overall matrix, and then inserting the submatrices into different positions of the overall matrix;
• adjusting the dimension of the overall matrix, acquiring the element information of the overall matrix, and generating control parameters for secondary scrambling;
• scrambling the merged overall matrix according to the row-state transition probability matrix and the column-state transition probability matrix, and simultaneously setting corresponding flag bits;
• and
• performing independent diffusion of elements on the overall matrix by using one of the chaotic sequences, and performing global diffusion on elements of the overall matrix by using the other chaotic sequences to obtain a final encrypted image.