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Background  The existing techniques for simultaneous encryption and compression of images refer lossy compression. Their reconstruction performances did not meet the accuracy of medical images because most of them have not been applicable to three-dimensional (3D) medical image volumes intrinsically represented by tensors.    Methods  We propose a tensor-based algorithm using tensor compressive sensing (TCS) to address these issues. Alternating least squares is further used to optimize the TCS with measurement matrices encrypted by discrete 3D Lorenz.    Results  The proposed method preserves the intrinsic structure of tensor-based 3D images and achieves a better balance of compression ratio, decryption accuracy, and security. Furthermore, the characteristic of the tensor product can be used as additional keys to make unauthorized decryption harder.    Conclusions  Numerical simulation results verify the validity and the reliability of this scheme.

Simultaneous encryption and compression of medical images based on optimized tensor compressed sensing with 3D Lorenz