Total Variation Based Oversampling of Noisy Images
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Measuring and Improving Image Resolution by Adaptation of the Reciprocal Cell
Journal of Mathematical Imaging and Vision
Total Variation Wavelet Inpainting
Journal of Mathematical Imaging and Vision
Edge-Forming Methods for Image Zooming
Journal of Mathematical Imaging and Vision
A joint demosaicking-zooming scheme for single chip digital color cameras
Computer Vision and Image Understanding
Image Compression with Anisotropic Diffusion
Journal of Mathematical Imaging and Vision
Edge-and-corner preserving regularization for image interpolation and reconstruction
Image and Vision Computing
Image Super-Resolution by TV-Regularization and Bregman Iteration
Journal of Scientific Computing
Reversible Interpolation of Vectorial Images by an Anisotropic Diffusion-Projection PDE
International Journal of Computer Vision
A Geometric PDE for Interpolation of M-Channel Data
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Color Image Restoration Using Nonlocal Mumford-Shah Regularizers
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Edge-driven Image Interpolation using Adaptive Anisotropic Radial Basis Functions
Journal of Mathematical Imaging and Vision
Vector-valued image interpolation by an anisotropic diffusion-projection PDE
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Super-resolution using sub-band constrained total variation
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Super-resolution with sparse mixing estimators
IEEE Transactions on Image Processing
Undecimated wavelet transform-based image interpolation
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part III
Variational method for super-resolution optical flow
Signal Processing
Partial Differential Equations for Zooming, Deinterlacing and Dejittering
International Journal of Computer Vision
Contour Stencils: Total Variation along Curves for Adaptive Image Interpolation
SIAM Journal on Imaging Sciences
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Towards PDE-Based image compression
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
PCM'05 Proceedings of the 6th Pacific-Rim conference on Advances in Multimedia Information Processing - Volume Part I
Greedy regression in sparse coding space for single-image super-resolution
Journal of Visual Communication and Image Representation
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We focus in this paper on some reconstruction/restoration methods whose aim is to improve the resolution of digital images. The main point here is to study the ability of such methods to preserve one-dimensional (1D) structures. Indeed, such structures are important since they are often carried by the image "edges." First we focus on linear methods, give a general framework to design them, and show that the preservation of 1D structures pleads in favor of the cancellation of the periodization of the image spectrum. More precisely, we show that preserving 1D structures implies the linear methods to be written as a convolution of the "sinc interpolation." As a consequence, we cannot cope linearly with Gibbs effects, sharpness of the results, and the preservation of the 1D structure. Second, we study variational nonlinear methods and, in particular, the one based on total variation. We show that this latter permits us to avoid these shortcomings. We also prove the existence and consistency of an approximate solution to this variational problem. At last, this theoretical study is highlighted by experiments, both on synthetic and natural images, which show the effects of the described methods on images as well as on their spectrum.