Joint Data Hiding and Partial Encryption of Compressive Sensed Streams

The paper proposes a method to secure the Compressive Sensing (CS) streams. It consists in protecting part of the measurements by a secret key and inserting the code into the rest. The secret key is generated via a cryptographically secure pseudo-random number generator (CSPRNG) and XORed with the measurements to be inserted. For insertion, we use a reversible data hiding (RDH) scheme, which is a prediction error expansion algorithm, modified to match the statistics of CS measurements. The reconstruction from the embedded stream conducts to visibly distorted images. The image distortion is controlled by the number of embedded levels. In our tests, the embedding on 10 levels results in $\approx 18 dB $ distortion for images of 256x256 pixels reconstructed with the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). A particularity of the presented method is on-the-fly insertion that makes it appropriate for the sequential acquisition of measurements by a Single Pixel Camera. On-the-fly insertion avoids the buffering of CS measurements for a subsequent standard encryption and generation of a thumbnail image.