This article proposes a new method for image separation into a linear combination of morphological components.
This method is applied to decompose an image into meaningful cartoon and textural layers and is used
to solve more general inverse problems such as image inpainting. For each of these components, a dictionary is
learned from a set of exemplar images. Each layer is characterized by a sparse expansion in the corresponding
dictionary. The separation inverse problem is formalized within a variational framework as the optimization of an
energy functional. The morphological component analysis algorithm allows to solve iteratively this optimization
problem under sparsity-promoting penalties. Using adapted dictionaries learned from data allows to circumvent
some difficulties faced by fixed dictionaries. Numerical results demonstrate that this adaptivity is indeed crucial
to capture complex texture patterns.
This article presents the first adaptive quasi minimax estimator for geometrically regular images in the white noise
model. This estimator is computed using a thresholding in an adapted orthogonal bandlet basis optimized for the noisy
observed image. In order to analyze the quadratic risk of this best basis denoising, the thresholding in an orthogonal
bandlets basis is recasted as a model selection process. The resulting estimator is computed with a fast algorithm whose
theoretical performance can be derived. This efficiency is confirmed through numerical experiments on natural images.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.