Abstract 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.

中文翻译：

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基于混沌 DWT 稀疏基和混沌 DCT 测量矩阵的图像安全压缩感知

摘要 本文提出了基于混沌离散小波变换(DWT)基和混沌离散余弦变换(DCT)测量矩阵相结合的安全压缩感知。在所提出的方案中，使用逻辑映射生成两个混沌序列，用于对常规DCT和原始DWT矩阵的行进行加扰，分别形成混沌测量矩阵和稀疏基矩阵。原始图像首先通过得到的混沌 DWT 矩阵转换为稀疏域信号。此后，通过获得的混沌 DCT 测量矩阵对所得信号进行压缩采样。