Fundamentals of digital image processing
Fundamentals of digital image processing
Digital image processing
An algorithmic comparison between square- and hexagonal-based grids
CVGIP: Graphical Models and Image Processing
Elements of information theory
Elements of information theory
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
Two-dimensional imaging
The image processing handbook (2nd ed.)
The image processing handbook (2nd ed.)
Digital image processing (3rd ed.): concepts, algorithms, and scientific applications
Digital image processing (3rd ed.): concepts, algorithms, and scientific applications
Fast Fourier Transform for Hexagonal Aggregates
Journal of Mathematical Imaging and Vision
Digital Image Processing
Digital Picture Processing
Edge Direction Preserving Image Zooming: A Mathematical and Numerical Analysis
SIAM Journal on Numerical Analysis
Wavelet families of increasing order in arbitrary dimensions
IEEE Transactions on Image Processing
Bayesian tree-structured image modeling using wavelet-domain hidden Markov models
IEEE Transactions on Image Processing
Adapted Total Variation for Artifact Free Decompression of JPEG Images
Journal of Mathematical Imaging and Vision
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Traditionally, discrete images are assumed to be sampled on a square grid and from a special kind of band-limited continuous image, namely one whose Fourier spectrum is contained within the rectangular “reciprocal cell” associated with the sampling grid. With such a simplistic model, resolution is just given by the distance between sample points.Whereas this model matches to some extent the characteristics of traditional acquisition systems, it doesn't explain aliasing problems, and it is no longer valid for certain modern ones, where the sensors may show a heavily anisotropic transfer function, and may be located on a non-square (in most cases hexagonal) grid.In this work we first summarize the generalizations of Fourier theory and of Shannon's sampling theorem, that are needed for such acquisition devices. Then we explore its consequences: (i) A new way of measuring the effective resolution of an image acquisition system; (ii) A more accurate way of restoring the original image which is represented by the samples. We show on a series of synthetic and real images, how the proposed methods make a better use of the information present in the samples, since they may drastically reduce the amount of aliasing with respect to traditional methods. Finally we show how in combination with Total Variation minimization, the proposed methods can be used to extrapolate the Fourier spectrum in a reasonable manner, visually increasing image resolution.