Wavelets and curvelets for image deconvolution: a combined approach

Authors:
Jean-Luc Starck;Mai K. Nguyen;Fionn Murtagh
Affiliations:
DAPNIA/SEDI-SAP, Service d'Astrophysique, CEA-Saclay, 91191 Gif sur Yvette, France;Equipe de Traitement des Images et du Signal, CNRS UMR 8051-ENSEA-Université de Cergy-Pontoise, 6, avenue du Ponceau, 95014 Cergy, France;School of Computer Science, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland
Venue:
Signal Processing - Special section: Security of data hiding technologies
Year:
2003

Citing 4
Cited 15

Multiresolution support applied to image filtering and restoration

Graphical Models and Image Processing
Image processing and data analysis: the multiscale approach

Image processing and data analysis: the multiscale approach
New multiscale transforms, minimum total variation synthesis: applications to edge-preserving image reconstruction

Signal Processing - Image and Video Coding beyond Standards
The curvelet transform for image denoising

IEEE Transactions on Image Processing

Compressive Algorithms--Adaptive Solutions of PDEs and Variational Problems

Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
A proximal iteration for deconvolving Poisson noisy images using sparse representations

IEEE Transactions on Image Processing
A fast multilevel algorithm for wavelet-regularized image restoration

IEEE Transactions on Image Processing
Shearlet-based deconvolution

IEEE Transactions on Image Processing
A SURE approach for digital signal/image deconvolution problems

IEEE Transactions on Signal Processing
Sparse representation based iterative incremental image deblurring

ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Restoration of Poissonian images using alternating direction optimization

IEEE Transactions on Image Processing
3-D Data Denoising and Inpainting with the Low-Redundancy Fast Curvelet Transform

Journal of Mathematical Imaging and Vision
A coordinate gradient descent method for l1-regularized convex minimization

Computational Optimization and Applications
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing

SIAM Journal on Scientific Computing
Alternating Direction Method for Image Inpainting in Wavelet Domains

SIAM Journal on Imaging Sciences
Image deconvolution using incomplete Fourier measurements

International Journal of Imaging Systems and Technology
Directionlet-based denoising of SAR images using a Cauchy model

Signal Processing
Harmonic analysis filtering techniques for forced and decaying homogeneous isotropic turbulence

Computers & Mathematics with Applications
A balanced combination of Tikhonov and total variation regularizations for reconstruction of piecewise-smooth signals

Signal Processing

Quantified Score

Hi-index	0.01

Visualization

Abstract

We propose in this paper a new deconvolution approach, which uses both the wavelet transform and the curvelet transform in order to benefit from the advantages of each. We illustrate the results with simulations.