Image Compression-Encryption Algorithms Combining Wavelet-based Compressive Sensing With Fractional Transforms

Compressive sensing, as a new signal processing theory, has been applied into various fields for the “less sampling” principle. However, compressive sensing in the field of image encryption is still at the primary stage, and the image encryption scheme based on compressive sensing are still not perfect. In order to enrich the applications of compressive sensing in image encryption, two new image encryption algorithms combining compressive sensing with fractional random transform or fractional angular transform respectively were designed. One is a double-image encryption-compression scheme based on compressive sensing and fractional random transform, which can decrease the image data and improve the efficiency of image encryption. The other is a color image encryption scheme combining 2D compressive sensing(2D CS) with discrete fractional angular transform, which can realize color image compression and encryption simultaneously. The main jobs are as follows:A double-image encryption-compression scheme based on compressive sensing and fractional random transform is proposed. Two original images are compressed and encrypted to be two intermediate results with compressive sensing, and then the two intermediate results are connected into an image. The resulting image is re-encrypted by Arnold transform and fractional random transform. In the process of decryption, the ciphertext could be decrypted by using the inverse fractional random transform firstly and then the decrypted image can be obtained by the smoothed 0l norm reconstruction algorithm.A 2D CS theory based on wavelet basis is studied, and a new color image encryption scheme combining 2D CS with fractional angular transform is proposed. Original color image is decomposed into Red, Green, and Blue components firstly. With the advantage of 2D CS, three components are compressed and encrypted to be three intermediate results, respectively. And then they are connected to be a large image. In order to enhance the security of the scheme, the large image is re-encrypted by the fractional angular transform. Correspondingly, the decryption process is the inverse of the encryption process. And the decrypted image could be obtained by taking the inverse fractional angular transform and the 0ANSL reconstruction algorithm.