  With the widespread sharing of personal face images in applications' public
databases, face recognition systems faces real threat of being breached by
potential adversaries who are able to access users' face images and use them to
intrude the face recognition systems. In this paper, we propose a novel privacy
protection method in the multiscale sparsified feature subspaces to protect
sensitive facial features, by taking care of the influence or weight ranked
feature coefficients on the privacy budget, named "Ranked Differential Privacy
(RDP)". After the multiscale feature decomposition, the lightweight Laplacian
noise is added to the dimension-reduced sparsified feature coefficients
according to the geometric superposition method. Then, we rigorously prove that
the RDP satisfies Differential Privacy. After that, the nonlinear Lagrange
Multiplier (LM) method is formulated for the constraint optimization problem of
maximizing the utility of the visualization quality protected face images with
sanitizing noise, under a given facial features privacy budget. Then, two
methods are proposed to solve the nonlinear 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 Gradient Descent (LMGD) numerical
method 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 0.2, the PSNR (Peak Signal-to-Noise Ratio) of the RDP is
about ~10 dB higher than (10 times as high as) the highest PSNR of all compared
methods.
