Secure compressive sensing of images based on combined chaotic DWT sparse basis and chaotic DCT measurement matrix

In this paper, secure compressive sensing based on a combination of the chaotic discrete wavelet transform (DWT) basis and chaotic discrete cosine transform (DCT) measurement matrix is proposed. In the proposed scheme, a logistic map is employed to generate two chaotic sequences that are used to scramble the rows of the conventional DCT and original DWT matrix to form a chaotic measurement matrix and sparse basis matrix, respectively. The original image is first transformed into a sparse domain signal by the obtained chaotic DWT matrix. Thereafter, the resulting signal is compressively sampled by the obtained chaotic DCT measurement matrix. Numerical experiments show that the proposed scheme not only achieves image encryption and compression simultaneously but also enlarges the key space and improves the quality of the reconstructed image compared to that of the conventional chaotic measurement matrix method.