Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Iterative reconstruction of multivariate band-limited functions from irregular sampling values
SIAM Journal on Mathematical Analysis
Nonlinear Analysis: Theory, Methods & Applications
Efficient numerical methods in non-uniform sampling theory
Numerische Mathematik
Advances in Gabor Analysis
Fast Implicit Active Contour Models
Proceedings of the 24th DAGM Symposium on Pattern Recognition
A convergent monotone difference scheme for motion of level sets by mean curvature
Numerische Mathematik
Universal Algorithms for Learning Theory Part I : Piecewise Constant Functions
The Journal of Machine Learning Research
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
IEEE Transactions on Image Processing
Image and Video Colorization Using Vector-Valued Reproducing Kernel Hilbert Spaces
Journal of Mathematical Imaging and Vision
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
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This paper concerns with nonuniform sampling and interpolation methods combined with variational models for the solution of a generalized color image inpainting problem and the restoration of digital signals. In particular, we discuss the problem of reconstructing a digital signal/image from very few, sparse, and complete information and from a substantially incomplete information, which will be assumed as the result of a nonlinear distortion. Differently from well known inpainting applications for the recovery of gray images, the proposed techniques apply to color images embedding blanks where only gray level information is given. As a typical and inspiring example, we illustrate the concrete problem of the color restoration of a destroyed art fresco from its few known fragments and some gray picture taken prior to the damage. Numerical implementations are included together with several examples and numerical results to illustrate the proposed method. The numerical experience suggests furthermore that a particular system of coupled Hamilton-Jacobi equations is well-posed.