Joint Data Hiding and Partial Encryption of Compressive Sensed Streams

TL;DR

The paper presents an on-the-fly reversible data hiding scheme tailored to compressive sensing streams from a single-pixel camera, where a subset of measurements is encrypted with a secret key and embedded into the remaining measurements using a modified prediction error expansion RDH. The framework uses a scrambled Hadamard sensing matrix and transmits a seed to enable reconstruction, enabling sequential acquisition without buffering and allowing distortion to be tuned by the number of inserted levels $n$ (with $n$ up to about $14$ in the study). The authors derive an insertion-capacity model and analyze the impact on dynamic range and data volume, validating the approach on synthetic sky images and real measurements; they report an average distortion around $18$ dB at $n=10$ for synthetic data and discuss security against error concealment attacks. The work offers a practical, low-overhead mechanism for protecting CS streams in streaming imaging applications, with explicit rate–distortion trade-offs and a framework for evaluating security implications.

Abstract

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.

Figures (14)

• Figure S1: Schema of the proposed scenario. (up) Data insertion: if information is available for embedding and the measurement is eligible, the modified measurement is computed and transmitted. If not, the measurement is shifted and transmitted. If information is no longer available for embedding, the current measurement is processed to be used for insertion. (down) Data extraction: if the user is authorised, the embedded information be extracted and the original measurements recovered. In the contrary case, the user is obliged to reconstruct the image using the reduced set of modified measurements
• Figure S2: Embedding process example on 7 bits.
• Figure S3: An example of measurement distribution for scrambled Hadamard matrix. The blue area delimited by the thresholds $-T$ and $T$ is the probability of insertable measurements.
• Figure :
• Figure S6: The distortion as a function of insertion levels in three instances: reconstruction from truncated measurements with no embedding (blue), marked measurements extended to contain the measurements to be embedded too (red), and including both embedding and truncation (black).