By Topic

A Fast Karhunen-Loeve Transform for Digital Restoration of Images Degraded by White and Colored Noise

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
A. K. Jain ; Department of Electrical Engineering, State University of New York

The Karhunen-Loeve (KL) transform is known to have certain properties which make it "optimal" for many "mean-square" signal processing applications [1]-[4]. Recently, it has been shown that a class of digital images may be represented by a set of boundary value stochastic difference equations in two dimensions [5]-[7]. If the boundary conditions of this class of images are fixed, then these equations lead to a fast KL transform algorithm. Here this fast KL transform is used for Wiener filtering of images degraded by white or colored noise. Comparisons with "Generalized Wiener Filtering" [1] and conventional Fourier domain filtering are made. It is shown that the two-dimensional Wiener filter is nonseparable so that two-dimensional generalized Wiener filtering is more elaborate than reported in [1]. It is also shown that certain fast KL filters give better signal-to-noise ratio than the conventional Fourier domain Wiener filter and enable determination of an easily computable performance bound. Recursive filtering equations for implementing the fast KL filter on two-dimensional images including both white and colored noise cases are given. These results show that recursive filtering algorithms for images are faster than the transform-domain algorithms and the one-step interpolator algorithm performs very close to the smoothing filter and can be implemented online by introducing a one-step delay.

Published in:

IEEE Transactions on Computers  (Volume:C-26 ,  Issue: 6 )