Ten lectures on wavelets
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
International Journal of Computer Vision
International Journal of Computer Vision
Convergence of an Iterative Method for Total Variation Denoising
SIAM Journal on Numerical Analysis
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Filtering, Segmentation, and Depth
Filtering, Segmentation, and Depth
Edge Direction Preserving Image Zooming: A Mathematical and Numerical Analysis
SIAM Journal on Numerical Analysis
ENO-Wavelet Transforms for Piecewise Smooth Functions
SIAM Journal on Numerical Analysis
Image replacement through texture synthesis
ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 3 - Volume 3
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
Subband-coded image reconstruction for lossy packet networks
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Total variation blind deconvolution
IEEE Transactions on Image Processing
The digital TV filter and nonlinear denoising
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Filling-in by joint interpolation of vector fields and gray levels
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
Recovery of corrupted image data based on the NURBS interpolation
IEEE Transactions on Circuits and Systems for Video Technology
Error Analysis for Image Inpainting
Journal of Mathematical Imaging and Vision
L0-Norm and Total Variation for Wavelet Inpainting
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Overcompressing JPEG Images with Evolution Algorithms
Proceedings of the 2007 EvoWorkshops 2007 on EvoCoMnet, EvoFIN, EvoIASP,EvoINTERACTION, EvoMUSART, EvoSTOC and EvoTransLog: Applications of Evolutionary Computing
Reconstructing Optical Flow Fields by Motion Inpainting
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
A fast optimization transfer algorithm for image inpainting in wavelet domains
IEEE Transactions on Image Processing
The discrete orthonormal Stockwell transform for image restoration
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
A New Multiscale Representation for Shapes and Its Application to Blood Vessel Recovery
SIAM Journal on Scientific Computing
A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method
SIAM Journal on Imaging Sciences
Total Variation as a Local Filter
SIAM Journal on Imaging Sciences
A Modified TV-Stokes Model for Image Processing
SIAM Journal on Scientific Computing
Alternating Direction Method for Image Inpainting in Wavelet Domains
SIAM Journal on Imaging Sciences
Geometrically Guided Exemplar-Based Inpainting
SIAM Journal on Imaging Sciences
A non-local MRF model for heritage architectural image completion
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
Image recovery from partial wavelet coefficients via sparse representation
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
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We consider the problem of filling in missing or damaged wavelet coefficients due to lossy image transmission or communication. The task is closely related to classical inpainting problems, but also remarkably differs in that the inpainting regions are in the wavelet domain. New challenges include that the resulting inpainting regions in the pixel domain are usually not geometrically well defined, as well as that degradation is often spatially inhomogeneous. We propose two related variational models to meet such challenges, which combine the total variation (TV) minimization technique with wavelet representations. The associated Euler-Lagrange equations lead to nonlinear partial differential equations (PDE's) in the wavelet domain, and proper numerical algorithms and schemes are designed to handle their computation. The proposed models can have effective and automatic control over geometric features of the inpainted images including sharp edges, even in the presence of substantial loss of wavelet coefficients, including in the low frequencies. Existence and uniqueness of the optimal inpaintings are also carefully investigated.