Denoising is always a challenge problem in natural image and geophysical data processing. From the point of view
of data assimilation, in this paper we consider the denoising of texture images in a scale space using a geometric
wavelet based nonlinear reaction-diffusion equation, in which a curvelet shrinkage is used as a regularization of
the diffusivity to preserve important features in the diffusion smoothing and a wave atom shrinkage is used as
a pseudo-observation in the reaction for enhancement of interesting oriented textures. We named the general
framework as image assimilation. The goal of the image assimilation is to link together these rich information
such as sparse constraint in multiscale geometric space in order to retrieve the state of images. As a byproduct,
we proposed a 2D wavelet-inspired numerical scheme for solving of the nonlinear diffusion. Experimental results
show the performance of the proposed model for texture-preserving denoising and enhancement.
This paper presents a refining estimation to control the process of adaptive mesh refinement (AMR) based on the
curvelet transform. The curvelet is a recently developed geometric multiscale system that could provide optimal
approximation to curve-singularity functions and sparse representation of wavefront phenomena. Utilizing these
advantages, we attempt to introduce the curvelet transform into AMR as a criterion estimate of refinement for adaptive
solving of the wave equation. Numerical simulations show that the proposed method could optimally capture interesting
areas where refinement is needed, so that a high accuracy result is obtained.
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.