RDP: Ranked Differential Privacy for Facial Feature Protection in Multiscale Sparsified Subspaces

With the widespread sharing of personal face images on the Internet, systems based on face recognition encounter the real threat of being breached by potential adversaries who are able to access individuals’ face images and use them to intrude the systems. In this article, we propose a novel privacy protection method in the sparsified multiscale feature subspaces to protect sensitive facial features, taking care of the influence or weight-ranked subspace coefficients on the privacy budget, named “ranked differential privacy (RDP).” After the multiscale subspaces’ decomposition, the lightweight Laplacian noise is added to the dimension-reduced sparsified subspaces’ coefficients according to the geometric superposition method. Then, we rigorously prove that the RDP satisfies <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{0}$ </tex-math></inline-formula>-differential privacy. After that, the nonlinear Lagrange multiplier method (LM) is formulated for the constraint optimization problem of maximizing the utility of protected face images of high-visualization quality with sanitizing noise, under a given privacy budget <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{0}$ </tex-math></inline-formula>. Then, two methods are proposed to solve the nonlinear Lagrangian multiplier method (LM) problem and obtain the optimal noise scale parameters: 1) the analytical normalization approximation (NA) method with identical average noise scale parameter for real-time online applications and 2) the LM optimization method via gradient descent (LMGD) to obtain the nonlinear solution through iterative updating for more accurate offline applications. Experimental results on two real-world datasets show that our proposed RDP outperforms other state-of-the-art methods: at a privacy budget of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{0} = 0.2$ </tex-math></inline-formula>, the peak signal-to-noise ratio (PSNR) of the optimized RDP is about ~10 dB higher than (10 times as high as) the highest PSNR of all state-of-the-art methods compared.