Journal Article10.1007/BF00932298
Partial differential equations and finite-difference methods in image processing, part 1: Image representation
110
TL;DR: In this article, the fast Karhunen-Loeve transform is extended to images with nonseparable or nearly isotropic covariance functions, or both, for image restoration, data compression, edge detection, image synthesis, etc.
read more
Abstract: Stochastic representation of discrete images by partial differential equation operators is considered. It is shown that these representations can fit random images, with nonseparable, isotropic covariance functions, better than other common covariance models. Application of these models in image restoration, data compression, edge detection, image synthesis, etc., is possible. Different representations based on classification of partial differential equations are considered. Examples on different images show the advantages of using these representations. The previously introduced notion of fast Karhunen-Loeve transform is extended to images with nonseparable or nearly isotropic covariance functions, or both.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Linear operators and stochastic partial differential equations in Gaussian process regression
Simo Särkkä
- 14 Jun 2011
TL;DR: An extension to Gaussian process (GP) regression models, where the measurements are modeled as linear functionals of the underlying GP and the estimation objective is a general linear operator of the process is discussed.
170
Motion picture restoration
Anil Kokaram
- 01 Jan 1998
TL;DR: In this article, a 3D multilevel median structure was proposed to suppress the impulsive distortion (Dirt and Sparkle or Blotches) and noise degradation in video sequences.
159
Introduction To The Special Issue On Partial Differential Equations And Geometry-driven Diffusion In Image Processing And Analysis
TL;DR: This work is presented to ensure timely dissemination of scholarly and technical work and to adhere to the terms and constraints invoked by each author's copyright.
154
Partial differential equations and finite difference methods in image processing--Part II: Image restoration
A. K. Jain,J. Jain +1 more
TL;DR: In this paper, the application of Partial Differential Equation (PDE) models for restoration of noisy images is considered and performance bounds based on PDE model theory are calculated and implementation tradeoffs of different algorithms are discussed.
126
Recursive Block Coding--A New Approach to Transform Coding
P. Farrelle,A. Jain +1 more
TL;DR: Improved performance of recursive block coding algorithms results in suppression of the block-boundary effect commonly observed in traditional transform coding techniques, illustrated by comparing RBC with cosine transform coding using both one- and twodimensional algorithms.
64
References
•Book
Stochastic Processes and Filtering Theory
Andrew H. Jazwinski
- 14 Mar 1970
TL;DR: In this paper, a unified treatment of linear and nonlinear filtering theory for engineers is presented, with sufficient emphasis on applications to enable the reader to use the theory for engineering problems.
7.9K
Discrete Cosine Transform
TL;DR: In this article, a discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed, which can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering.
5.1K
•Book
Partial Differential Equations
Paul Garabedian
- 01 Dec 1964
TL;DR: The method of power series Equations of the first order Classification of partial differential equations Cauchy's problem for equations with two independent variables The Dirichlet and Neumann problems as mentioned in this paper.
1K
Two-dimensional Bayesian estimate of images
A. Habibi
- 01 Jul 1972
TL;DR: A dynamic model for pictorial data that can be represented by a random field of an exponential autocorrelation function is developed and is used to realize a two-dimensional recursive filter that gives a Bayesian-estimate of the pictorialData from a noisy observation of the data.
244