  We consider the problem of estimating a low-rank signal matrix from noisy
measurements under the assumption that the distribution of the data matrix
belongs to an exponential family. In this setting, we derive generalized
Stein's unbiased risk estimation (SURE) formulas that hold for any spectral
estimators which shrink or threshold the singular values of the data matrix.
This leads to new data-driven spectral estimators, whose optimality is
discussed using tools from random matrix theory and through numerical
experiments. Under the spiked population model and in the asymptotic setting
where the dimensions of the data matrix are let going to infinity, some
theoretical properties of our approach are compared to recent results on
asymptotically optimal shrinking rules for Gaussian noise. It also leads to new
procedures for singular values shrinkage in finite-dimensional matrix denoising
for Gamma-distributed and Poisson-distributed measurements.
