Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
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
Stochastic models for generic images
Quarterly of Applied Mathematics
Realistic image synthesis using photon mapping
Realistic image synthesis using photon mapping
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Modern Digital Halftoning
On Advances in Statistical Modeling of Natural Images
Journal of Mathematical Imaging and Vision
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing
Journal of Scientific Computing
IBM Journal of Research and Development
Image Decomposition into a Bounded Variation Component and an Oscillating Component
Journal of Mathematical Imaging and Vision
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Reconstructing images from their most singular fractal manifold
IEEE Transactions on Image Processing
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
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A new mathematical image model is introduced using the photographic process as the starting point. Images are represented as infinite sequences of photons allowing analysis at arbitrarily high resolution and leading to novel computational methods for processing, representation, transmission and storage of images. The resulting space of infinite photographs is proved to have a metric structure and to be intimately connected with bounded Borel measures. Theorems are proved indicating that the imaging power of the photographic process exceeds function spaces in the high resolution limit; this implies in particular that natural photographic images need to be modelled by generalized functions. Furthermore, computational results are presented to illustrate the novel algorithms based on photon sequences. The algorithms include stochastic halftoning, representation of cartoon images with outlines, anti-aliasing, blurring and singularity extraction.