Practical Secure OMP Computation and Its Application to Image Modeling

In this paper, we propose the secure computation of sparse coding based on a random unitary transform. Cloud computing is spreading to many application fields including services that use sparse coding. This situation raises many new privacy concerns. The proposed scheme provides a practical Orthogonal Matching Pursuit (OMP) algorithm that allows computation on encrypted signals. We prove, theoretically, that the proposal has exactly the same sparse coefficient estimation performance as the unencrypted variant of the OMP algorithm. We apply it to image modeling based on an image patch model. Finally, we demonstrate its performance on synthetic data and natural images.