Image compression and encryption algorithm with wavelet-transform-based 2D compressive sensing

By combining a wavelet transform with chaos scrambling, an image compression and encryption algorithm based on 2D compressive sensing is designed. The wavelet transform is employed to obtain the sparse representation of a plaintext image. The sparse image is measured in two orthogonal directions by compressive sensing. Then, the result of 2D compressive sensing is confused by the Arnold transform and the random pixel scrambling. The combination of four-dimensional chaos and logistic map is exploited to generate the first row of the key-controlled circulant matrix. The proposed algorithm not only carries out image compression and encryption simultaneously, but also reduces the consumption of the key by controlling the generation of measurement matrix. Experimental results reveal that the proposed image compression and encryption algorithm is resistant to noise attacks with good compression performance and high key sensitivity.