  We propose a data-dependent denoising procedure to restore noisy images.
Different from existing denoising algorithms which search for patches from
either the noisy image or a generic database, the new algorithm finds patches
from a database that contains only relevant patches. We formulate the denoising
problem as an optimal filter design problem and make two contributions. First,
we determine the basis function of the denoising filter by solving a group
sparsity minimization problem. The optimization formulation generalizes
existing denoising algorithms and offers systematic analysis of the
performance. Improvement methods are proposed to enhance the patch search
process. Second, we determine the spectral coefficients of the denoising filter
by considering a localized Bayesian prior. The localized prior leverages the
similarity of the targeted database, alleviates the intensive Bayesian
computation, and links the new method to the classical linear minimum mean
squared error estimation. We demonstrate applications of the proposed method in
a variety of scenarios, including text images, multiview images and face
images. Experimental results show the superiority of the new algorithm over
existing methods.
