19 research outputs found
Adaptive Image Denoising by Targeted Databases
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.Comment: 15 pages, 13 figures, 2 tables, journa
On the Contractivity of Plug-and-Play Operators
In plug-and-play (PnP) regularization, the proximal operator in algorithms
such as ISTA and ADMM is replaced by a powerful denoiser. This formal
substitution works surprisingly well in practice. In fact, PnP has been shown
to give state-of-the-art results for various imaging applications. The
empirical success of PnP has motivated researchers to understand its
theoretical underpinnings and, in particular, its convergence. It was shown in
prior work that for kernel denoisers such as the nonlocal means, PnP-ISTA
provably converges under some strong assumptions on the forward model. The
present work is motivated by the following questions: Can we relax the
assumptions on the forward model? Can the convergence analysis be extended to
PnP-ADMM? Can we estimate the convergence rate? In this letter, we resolve
these questions using the contraction mapping theorem: (i) for symmetric
denoisers, we show that (under mild conditions) PnP-ISTA and PnP-ADMM exhibit
linear convergence; and (ii) for kernel denoisers, we show that PnP-ISTA and
PnP-ADMM converge linearly for image inpainting. We validate our theoretical
findings using reconstruction experiments.Comment: Errors in the proof of Lemma 1 and the statement of Theorem 2 were
identified after the publication; these have been rectified in the revised
version (v2